202110181-APEX-STUDENT-WORKBOOK-MATHEMATICS-G06-PART1

Maths Workbook_6_P_1.pdf 1 18-10-2019 17:51:06 Name: ___________________________________ Section: ________________ Roll No.: _________ School: __________________________________

TABLE OF CONTENTS 1 KNOWING OUR NUMBERS 1 1.1 INTRODUCTION, ESTIMATION AND COMPARING NUMBERS 1 1.2 ESTIMATION AND ROUNDING OFF NUMBERS 5 1.3 PLACE VALUE OF LARGER NUMBERS 8 1.4 INTERNATIONAL SYSTEM OF NUMERATION 14 1.5 LARGE NUMBERS USED IN DAILY SITUATIONS 18 2 WHOLE NUMBERS 20 2.1 REPRESENTATION OF WHOLE NUMBERS ON NUMBER LINE 20 2.2 PROPERTIES OF WHOLE NUMBERS 23 2.3 PATTERN IN WHOLE NUMBERS 28 3 PLAYING WITH NUMBERS 31 3.1 DIVISIBILITY RULE 31 3.2 FACTORS 36 3.3 PRIME FACTORIZATION 39 3.4 COMMON FACTORS 42 3.5 COMMON MULTIPLES 45 3.6 RELATIONSHIP BETWEEN LCM AND HCF 47 3.7 DIVISIBILITY RULES FOR 4, 8 AND 11 49 4 BASIC GEOMETRICAL IDEAS 52 4.1 POINT, LINE SEGMENT, LINE AND RAY 52 4.2 CURVE AND POLYGONS 56 4.3 ANGLE 62 4.4 TRIANGLE AND QUADRILATERAL 66 4.5 CIRCLE 71

5 MEASURES OF LINES AND ANGLES 76 5.1 MEASURE OF A LINE SEGMENT 76 5.2 MEASURE OF AN ANGLE 79 5.3 INTERSECTING LINES, PERPENDICULAR LINES AND PARALLEL LINES 86 7 FRACTIONS AND DECIMALS 91 7.1 TYPES OF FRACTIONS 91 7.2 EQUIVALENT FRACTIONS 99 7.3 ORDERING, ADDITION AND SUBTRACTION OF FRACTIONS 102 7.4 PLACE VALUES IN A DECIMAL NUMBER AND ORDERING OF DECIMALS 106 7.5 ADDITION AND SUBTRACTION OF DECIMAL FRACTIONS 109 PROJECT BASED QUESTIONS 112 ADDITIONAL AS BASED PRACTICE QUESTIONS 114

CHAPTER 1 KNOWING OUR NUMBERS EXERCISE 1.1 INTRODUCTION, ESTIMATION AND COMPARING NUMBERS 1.1.1 Key Concepts i. The smallest four–digit number is 1000 (one thousand). ii. In the international system of numeration, commas are placed after every 3 digits starting from the right. The commas after 3rd and 6th digits separate thousands and millions respectively. 1.1.2 Additional Questions Objective Questions 1. [AS3] The largest number formed by the digits 8, 0, 5 and 7 is . (A) 8057 (B) 8570 (C) 8507 (D) 8750 2. [AS3] The smallest number among 3457, 3475, 3745, and 3754 is . (A) 3457 (B) 3475 (C) 3754 (D) 3745 3. [AS3] The ascending order of the numbers 609054; 600954; 605094; 690054 is . (A) 690054; 609054; 600954; 605094 (B) 600954; 605094; 609054; 690054 (C)605094; 600954; 690054; 609054 (D)690054; 609054; 605094; 600954 EXERCISE 1.1. INTRODUCTION, ESTIMATION AND COMPARING NUMBERS 1

4. [AS3] 794532 in words is . (A) Seventy nine thousand, forty five hundred and thirty two (B) Seven hundred and ninety four thousand fifty three hundred and two (C)Seven lakhs ninety four thousand five hundred and thirty two (D)None of these 5. [AS3] Nine crores three lakhs four thousand twenty three in figures is . (A) 9, 03, 04, 023 (B) 9, 34, 23000 (C)9, 00, 03, 423 (D)None of these 6. [AS1] The difference between the greatest and the smallest numbers formed by the digits 8, 0, 5 and 7 is . (A) 7632 (B) 3672 (C) 2367 (D) 2673 7. [AS1] The difference between the greatest and the smallest numbers among 3457, 3475, 3745 and 3754 is . (A) 297 (B) 197 (C) 329 (D) 927 Short Answer Type Questions 8(i) [AS3] Identify the greatest number among each of the following groups of numbers. a) 89056, 80956, 80596, 80569 b) 73214, 75432, 74321, 82341 (ii) [AS3] Identify the smallest number among each of the following groups of numbers. a) 70956, 70596, 70659, 70659, 70965 b) 60034, 60431, 60975, 60100, 60965 c) 98765, 95678, 85967, 89567, 85679 EXERCISE 1.1. INTRODUCTION, ESTIMATION AND COMPARING NUMBERS 2

9(i) [AS3] Identify the greatest and the smallest numbers among the following. a) 5478, 5487, 5468, 549 b) 8645, 879, 86583, 86561 (ii) [AS3] Write the numbers in ascending order: 5489, 54810, 54328, 54867 10(i) [AS3] Arrange the following numbers in ascending order. a) 342451, 340251, 304251, 324051, 324501 b) 76581, 56781, 18765, 18567, 18576, 15867 (ii) [AS3] Arrange the following numbers in descending order. a) 84251, 85432, 85234, 84532, 82564 b) 36074, 36470, 34670, 34760, 30674 c) 54032, 54320, 50342, 50234, 52034 11(i) [AS3] Write the following numbers in words. a) 96782 : ––––––––––––––––––––––––––––––– b) 500001 : –––––––––––––––––––––––––––––– (ii) [AS3] Write the following numbers in figures. a) Ninety thousand seventeen: ––––––––––– b) Seventy eight thousand two hundred and one: ––––––––– c) Eighty five crore eighty five: –––––––––––––– Long Answer Type Questions 12 [AS1] (i) How many 5 – digit numbers are there in all? (ii) How many 7 – digit numbers are there in all? 13 [AS1] (i) Find the difference between the number 279 and that obtained on reversing its digits. EXERCISE 1.1. INTRODUCTION, ESTIMATION AND COMPARING NUMBERS 3

(ii) Form the largest and the smallest 4 – digit numbers using each of the digits 7, 1, 0 and 5only once and find their difference. 14 [AS3] Form eight 5 – digit numbers using the digits 5, 0, 2, 8 and 3. Find the largest and the smallest numbers among them. EXERCISE 1.1. INTRODUCTION, ESTIMATION AND COMPARING NUMBERS 4

EXERCISE 1.2 ESTIMATION AND ROUNDING OFF NUMBERS 1.2.1 Key Concepts i. Estimation and rounding off numbers: We usually round off the numbers to the nearest 10 s, 100 s, 1000 s, 10000 s . . . . . . etc. ii. Rounding off the numbers to the nearest tens: 81 is nearer to 80 than to 90. So, 81 will be rounded off to 80. 87 is nearer to 90 than to 80. So, 87 will be rounded off to 90. 85 is at equal distance from 80 and 90 but by convention, it is rounded off to 90. 1.2.2 Additional Questions Objective Questions 1. [AS3] By rounding off the number 79085 to the nearest thousands, we get . . (A) 79000 (B) 79100 . (C) 80000 (D) 79080 2. [AS3] By rounding off the number 60018 to the nearest hundreds, we get (A) 60010 (B) 60100 (C) 60000 (D) 60020 3. [AS3] The number that can be rounded off to the nearest tens as 54320 is (A) 54329 (B) 54318 (C) 54313 (D) 54309 4. [AS3] 1 × 105 + 8 × 104 + 3 × 101 + 8 = . (A) 183800 (B) 108308 (C) 180308 (D) 180038 EXERCISE 1.2. ESTIMATION AND ROUNDING OFF NUMBERS 5

5. [AS3] 346005 = . (A) 3 × 105 + 4 × 104 + 6 × 103 + 5 (B) 3 × 104 + 4 × 103 + 6 × 102 + 5 (C)3 × 106 + 4 × 105 + 6 × 104 + 5 (D)3 × 106 + 4 × 105 + 6 × 104 + 5 × 103 6. [AS1] The difference between the place values of 5 in the number 857245 is . (A) 39906 (B) 50000 (C) 49975 (D) 49995 7. [AS2] If 95 is rounded off to nearest tens, the result is . (A) 100 (B) 90 (C)90 or 100 (D)None of these 8. [AS2] The smallest number that can be rounded off to the nearest thousands as 6000 is . (A) 5600 (B) 5300 (C) 5900 (D) 5500 9. [AS2] The greatest number that can be rounded off to the nearest hundreds as 600 is . . (A) 599 (B) 550 (C) 580 (D) 540 10. [AS2] The number of numbers which when rounded off to the nearest tens give 200 is (A) 9 (B) 10 (C) 8 (D) 7 Very Short Answer Type Questions . 11 [AS3] Fill in the blanks. (i) 5 × 105 + 4 × 104 + 3 × 101 + 7 = EXERCISE 1.2. ESTIMATION AND ROUNDING OFF NUMBERS 6

(ii) 8 × 104 + 3 = . (iii) 4 × 106 + 7 × 105 + 6 × 104 + 8 × 103 + 9 × 102 + 3 × 101 + 2 = . (iv) 7 × 105 + 9 × 103 + 1 = . (v) 6 × 104 + 7 × 103 + 8 × 102 + 9 = . Short Answer Type Questions 12 [AS1] Round off the following numbers to the nearest hundreds. (i) 964 (ii) 45,634 13 (i) [AS3] Round off the numbers to the nearest hundreds. a) 876 b) 1250 (ii) [AS3] Round off the numbers 8126 and 3615 to the nearest thousands. 14(i) [AS3] Expand: 5812 and 4080 (ii) [AS3] Expand: 44444 and 20052 EXERCISE 1.2. ESTIMATION AND ROUNDING OFF NUMBERS 7

EXERCISE 1.3 PLACE VALUE OF LARGER NUMBERS 1.3.1 Key Concepts i. It is difficult to read large numbers such as 25240, 12200320 in crores, lakhs and thousands. Therefore, we use ‘comma’ (,) to read and write such large numbers. Ex: 25,240 and 1,22,00,320. ii. It is comparatively easy to read large numbers written using commas. Places Number No. of digits Ten Crores 9 10,00,00,000 8 Crores 1,00,00,000 7 Ten Lakhs 6 10,00,000 5 Lakhs 1,00,000 Ten Thousands 10,000 Thousands 1,000 4 Hundreds 100 3 Tens 10 2 Ones 1 1 EXERCISE 1.3. PLACE VALUE OF LARGER NUMBERS 8

1.3.2 Additional Questions Objective Questions . 1. [AS3] 8, 36, 45, 321 in words is (A) Eight hundred and thirty six lakhs, forty five thousand three hundred and twenty one (B) Eight crore thirty six lakhs forty five thousand three hundred and twenty one (C)Eighty three crores sixty four lakhs five thousand three hundred and twenty one (D)None of these . 2. [AS3] Thirty five crores and eight in figures is (B) 35, 800 (A) 35, 008 (C)35, 00, 00, 008 (D)35, 00, 008 3. [AS3] 65480037 written in the Indian system of numeration is . (A) 6, 54, 80, 037 (B) 65, 480, 037 (C)6, 5480, 037 (D)65480, 037 4. [AS3] The place value of ‘5’ in 8574321 is . (A) 50, 00, 000 (B) 50, 000 (C)5, 00, 00, 000 (D)5, 00, 000 5. [AS1] The difference between the place value and the face value of ‘4’ in the number 693451 is . (A) 404 (B) 396 (C) 400 (D) 4 Very Short Answer Type Questions 6 [AS1] Answer the following questions in one sentence. (i) Find the difference between the place value and face value of 7 in 45072. (ii) Find the product of the place values of two fives in 4505. (iii) Find the sum of the place values of digits 3 and 7 in the number 9030678. (iv) Find the product of the place values of two 3’s in 363. EXERCISE 1.3. PLACE VALUE OF LARGER NUMBERS 9

(v) Find the difference of the place values of two fives in 3565. 7 [AS2] Answer the following questions in one sentence. (i) Show that if 450 is rounded off to the nearest hundreds, the result is 500. (ii) Show that 796 – 314 = 500 (If the numbers are estimated and rounded off to the nearest hundreds.) (iii) Which is the least number when rounded off to the nearest hundreds becomes equal to 300? (iv) Which is the greatest number that when rounded off to the nearest hundreds becomes equal to 300? (v) If 3a4 is rounded off to the nearest hundreds it becomes equal to 400. What are the possible values of a? 8 [AS3] Choose the correct answer. (i) The greatest among the given numbers is _________. (A) 52163 (B) 52247 (C) 52316 (D) 52168 (ii) The greatest among the given numbers is _________. (A) 84125 (B) 84213 (C) 84203 (D) 84230 (iii) The smallest among the given numbers is ______. (A) 21362 (B) 21358 (C) 21346 (D) 21320 (iv) The smallest among the given numbers is ______. (A) 30152 (B) 30015 (C) 30005 (D) 30021 (v) The number greater than 61249 is _____. (B) 61214 (A) 61237 (C) 61241 (D) 62114 9 [AS3] Answer the following questions in one sentence. (i) Write 21, 395 in words. EXERCISE 1.3. PLACE VALUE OF LARGER NUMBERS 10

(ii) Write 5, 24, 95, 628 in words. (iii) Write 6, 32, 47, 192 in words. (iv) Write 12, 80, 001 in words. (v) Write 10, 00, 00, 101 in words. 10 [AS3] Answer the following questions in one sentence. (i) Write in numerals: Two lakhs twenty two thousand and two (ii) Write in numerals: Three crores five thousand and eight (iii) Write in numerals: Forty two thousand four hundred and forty two (iv) Write in numerals: Ninety lakhs eighty six thousand and one (v) Write in numerals: Thirty five crore five hundred and thirty six 11 [AS3] Fill in the blanks. (i) A paper bundle has 4000 papers. 3298 bundles have papers. (Mark commas). [AS3] Choose the correct answer. (ii) The number that is correctly marked with commas is _____. (A) 120, 598, 2, 45 (B) 12, 05, 98, 245 (C)1, 20, 59, 82, 45 (D)1, 20, 598, 245 [AS3] Answer the following questions in one sentence. (iii) Write the numbers using commas: a) 21302461 b) 53401296 (iv) Rewrite the statement using commas in the number: The population of a country is 602841192. (v) Write the number 2310120004 using commas. 12 [AS3] Answer the following questions in one sentence. (i) Express the number in expanded form: 52405678 (ii) Write the number in short form: 3000000 + 200000 + 80 + 2 EXERCISE 1.3. PLACE VALUE OF LARGER NUMBERS 11

(iii) Expand 56230. (iv) Expand 10000012. (v) 6000000 + 400000 + 3000 + 9 in short is . 13 [AS3] Fill in the blanks. (i) Eight lakhs fifty six thousand two hundred and thirty six in figures is . (ii) Seventy three lakhs and four in figures is . (iii) 9, 57, 008 in figures is . (iv) The greater of the numbers 3, 45, 987 and 3, 45, 978 is . . (v) The smaller of the numbers 7, 65, 431 and 7, 66, 432 is 14 [AS3] Answer the following questions in one sentence. (i) Write the number using commas according to the places of its digits. 82310642 (ii) Arrange the digits of the number in a place value chart: 5631028 (iii) Write the number in a place value chart: 623102324 (iv) Write the number in a place value chart: Four lakhs fifty nine thousand three hundred (v) Write the number in a place value chart: Two crores thirty three lakhs seventy thousand and sixty eight 15 [AS4] Answer the following questions in one sentence. (i) What is the cost of a building with 20 flats, if each flat costs Rs. 30, 00, 000? (ii) How many people are there in a region, if each city has 98, 900 people and there are 29 cities in the region? (iii) A rose garden exports 87, 24, 000 roses in 30 days. How many roses will it export in a day? (iv) A bakery gets Rs. 2, 12, 182 a day and its expenditure per day is Rs. 1, 86, 002. What is its profit? (v) Ashok has a house worth Rs. 52, 81, 000, a plot worth Rs. 15, 21, 000 and a land that costs Rs. 40, 20, 800. What is the total worth of his property? EXERCISE 1.3. PLACE VALUE OF LARGER NUMBERS 12

Short Answer Type Questions 16(i) [AS3] Form the greatest and the smallest 5–digit numbers using the digits 4, 0, 3, 8 and 7. (ii) [AS3] Using the digits 9, 8, 7, 6, 5 and 0 form the smallest and the greatest six–digit numbers. EXERCISE 1.3. PLACE VALUE OF LARGER NUMBERS 13

EXERCISE 1.4 INTERNATIONAL SYSTEM OF NUMERATION 1.4.1 Key Concepts i. In international system, the periods are ones, tens, hundreds, thousands and millions. ii. One million is a thousand thousands or ten lakhs. iii. Commas are used to mark thousands and millions. 1.4.2 Additional Questions Objective Questions 1. [AS3] The number 765903412 using commas in the international system of numeration is . (A) 765, 903, 412 (B) 76, 59, 03, 412 (C)76, 590, 341, 2 (D)765, 90, 34, 412 2. [AS3] The number 100432869 in words in the international system of numeration is . (A) One million four hundred thirty two thousand eight hundred and sixty nine (B) One billion, four hundred thirty two thousand eight hundred sixty nine (C)One hundred million four hundred thirty two thousand eight hundred and sixty nine (D)One thousand million four hundred thirty two thousand eight hundred and sixty nine 3. [AS3] The place value of ‘6’ in 4832679150 in the international system of numeration is . (A) 6 hundred thousand (B) 60 thousand (C)6 thousand thousand (D)6 million 4. [AS3] The digit in the ten millions place in 924617380 is . (A) 9 (B) 2 (C) 4 (D) 6 EXERCISE 1.4. INTERNATIONAL SYSTEM OF NUMERATION 14

5. [AS3] In the international system of numeration the place that comes after hundred thousands is . (A) Millions (B) Billions (C) Lakhs (D)Ten billions Very Short Answer Type Questions 6 [AS3] Choose the correct answer. (i) 546321 in the international system of numeration is –––––––––––––. (A) 5, 46, 321 (B) 54, 63, 21 (C)5, 463, 21 (D)546, 321 (ii) 80004321 in the international system of numeration is –––––––––––––. (A) 80, 004, 321 (B) 800, 043, 21 (C)80, 00, 43, 21 (D)8000, 4321 (iii) 7896543210 in the international system of numeration is ––––––––––––. (A) 7, 896, 543, 210 (B) 789, 654, 321, 0 (C)78, 96, 54, 32, 10 (D)7, 89, 65, 43, 210 (iv) 68543721 in the international system of numeration is –––––––––––––. (A) 6, 85, 43, 721 (B) 6854, 3721 (C)68, 54, 37, 21 (D)68, 543, 721 (v) 94382657 in the international system of numeration is –––––––––––––. (A) 943, 82, 657 (B) 94, 382, 657 (C)9, 438, 265, 7 (D)94, 38, 2, 657 7 [AS5] Choose the correct answer. (i) The place value of the underlined digit in 543218943 in the international system of numeration is _______. (A) 2 lakhs (B) 2 hundred thousand (C)2 millions (D)2 billions EXERCISE 1.4. INTERNATIONAL SYSTEM OF NUMERATION 15

(ii) The place value of the underlined digit (in the international system) in the number 73453219 is _______. (A) 30 millions (B) 30 millions (C)30 lakhs (D)3 crores (iii) The digit in the ten millions place of the number 943285610 is _______. (A) 9 (B) 4 (C) 3 (D) 2 (iv) The digit in the hundred millions place of the number 8734621590 is ______. (A) 8 (B) 4 (C) 3 (D) 7 (v) The place value of the underlined digit in 98674325 in the international system of numeration is _______. (A) 8 millions (B) 8 hundred thousands (C)80 lakhs (D)8 billions Short Answer Type Questions 8 [AS3] Rewrite the following using commas and also write in words in the international system of numeration. (i) 74381645 (ii) 8437258120 9(i) [AS3] Rewrite the following numbers in words in the international system of numeration. a) 173425689 b) 67894321 (ii) [AS3] Rewrite the following numbers in words in both the Indian and international systems of numeration. a) 50000348 b) 7546300 EXERCISE 1.4. INTERNATIONAL SYSTEM OF NUMERATION 16

10 [AS4] The population of Telangana in 2011 was 35193978. Rewrite the above statement using commas in both the systems of numeration. EXERCISE 1.4. INTERNATIONAL SYSTEM OF NUMERATION 17

EXERCISE 1.5 LARGE NUMBERS USED IN DAILY SITUATIONS 1.5.1 Key Concepts i. Remember that kilo means 1000, centi means 100th part and milli means 1000th part. ii. 1 kilometre = 1000 metres iii. 1 metre = 100 centimetres iv. 1 metre = 1000 millimetres 1.5.2 Additional Questions Objective Questions 1. [AS4] If a car travels 45 km in 1 hour, then the distance (in metres) covered by the car in 2 hours is . (A) 90 km (B) 9000 m (C)90000 m (D)900000 m 2. [AS4] If 20 ml of milk is used in making one cup of tea, then the quantity (in litres) of milk required to make 550 cups of tea is . (A) 11000 l (B) 11 l (C) 110 l (D)1.1 l 3. [AS4] By selling a pen, a shop keeper gets a profit of 80 paise. The total profit he earns in a month by selling 2000 pens is . (A) Rs.16 (B) Rs.160 (C) R s.1.6 (D) R s.1600 4. [AS4] If a motor cycle can travel 65 km with one litre of petrol, then the quantity of petrol required to cover a distance of 1527.5 km is . (A) 20 l (B) 23 l (C)23.5 l (D)25 l EXERCISE 1.5. LARGE NUMBERS USED IN DAILY SITUATIONS 18

5. [AS4] The population of a city is 2, 37, 48, 856 out of which 1, 12, 34, 567 are female. Then the male population of the city is . (A) 1, 25, 14, 289 (B) 1, 21, 54, 389 (C)1, 25, 41, 389 (D)1, 25, 13, 489 Short Answer Type Questions 6(i) [AS4] A car travels at a speed of 60 km per hour. Find the distance (in cm) travelled by car in 4 hours. (ii) [AS4] A paper weighs 2 g and a book contains 385 such pages. Find the weight of 15 such books. 7(i) [AS4] In Movie Arts Association (MAA) elections 2015, the elected candidate got 237 votes and the defeated candidate got 152 votes. By how many votes did the elected candidate win the election? (ii) [AS4] A T.V. manufacturing company earns a profit of Rs.4, 850 on selling one T.V. set. Find the total profit the company earns on selling 8000 T.V. sets. 8 [AS4] The bike manufacturing company HERO manufactures 1250 bikes per day. Find the total number of bikes manufactured in the months of January and February of the year 2012. EXERCISE 1.5. LARGE NUMBERS USED IN DAILY SITUATIONS 19

CHAPTER 2 WHOLE NUMBERS EXERCISE 2.1 REPRESENTATION OF WHOLE NUMBERS ON NUMBER LINE 2.1.1 Key Concepts Natural Numbers i. The numbers used for counting are called natural numbers. The set of natural numbers is denoted by “N”, N = {1, 2, 3, 4, . . . ..}. ii. If we add ‘1’ to any natural number, we get the next natural number. iii. The next number of any natural number is called its successor and the number just before a natural number is called its predecessor. iv. For example, the successor of 15 is 16 and its predecessor is 14. v. The number ‘1’ has no predecessor in natural numbers. Whole Numbers i. Whole numbers: We include zero to the collection of natural numbers. The natural numbers along with zero form the collection of whole numbers. ii. The set of whole numbers is represented as W = {0, 1, 2, 3, 4, . . . . . . . . .}. iii. Representation of Whole numbers on number line: The number line for whole numbers is iv. On the number line the successor of any number lies to the right of that number. 2.1.2 Additional Questions Objective Questions 1. [AS3] The least whole number is . (A) –1 (B) 0 (C) 1 (D)Cannot be said EXERCISE 2.1. REPRESENTATION OF WHOLE NUMBERS ON NUMBER LINE 20

2. [AS3] The natural number which is not a whole number is . (A) –1 (B) 0 (C) 1 (D)Does not exist 3. [AS3] The whole number which is not a natural number is . (A) –1 (B) 0 (C) 1 (D)Does not exist 4. [AS3] The successor of 12 lies to the of 14. (A) Left (B) Right (C) Above (D) Below 5. [AS3] The predecessor of 10 lies to its side. (A) Left (B) Right (C) Above (D) Below Very Short Answer Type Questions 6 [AS5] Answer the following questions in one sentence. (i) Identify the whole number ‘P’ represented on the number line given: (ii) Identify the whole number ‘x’ represented on the number line given: 21 (iii) Represent q = 6 on the number line. (iv) Represent x = 8 on the number line. (v) Find the value of ‘s’ on the given number line. EXERCISE 2.1. REPRESENTATION OF WHOLE NUMBERS ON NUMBER LINE

Short Answer Type Questions 7(i) [AS5] a) Represent the number 7 on the number line. b) Represent the successor of 11 on the number line. (ii) [AS5] Identify the missing numbers on the number line. 8(i) [AS5] Find the following using the number line. a) 2 × 8 b) 3 + 4 + 7 (ii) [AS5] Find the following using number line: a) 8 + 5 + 6 b) 15 − 8 c) 3 × 4 9(i) [AS5] Mark the following numbers on the number line and fill in the blanks. Write which one lies to the right and which one to the left. 28 (ii) [AS5] Mark the following on the number line and fill in the blanks using >(or) <. a) 4 6 b) 12 9 EXERCISE 2.1. REPRESENTATION OF WHOLE NUMBERS ON NUMBER LINE 22

EXERCISE 2.2 PROPERTIES OF WHOLE NUMBERS 2.2.1 Key Concepts i. Whenever we add two numbers we move on the number line towards right starting from any of them. ii. We move towards left in case of subtraction. iii. The sum of any two whole numbers is always a whole number. The collection of whole numbers is closed under addition. This property is known as the closure property of addition for whole numbers. iv. The product of any two numbers is also a whole number. v. The collection of whole numbers is closed under multiplication. vi. Addition is commutative for whole numbers. vii. Multiplication is commutative for whole numbers. viii. Whole numbers are not closed under subtraction and division. ix. Addition and multiplication are associative for whole numbers. x. Multiplication is distributive over addition for whole numbers. xi. 0 is the additive identity and 1 is the multiplicative identity of whole numbers. xii. Division of a whole number by zero does not give a known number as answer. So, division by zero is not defined. 2.2.2 Additional Questions Objective Questions 1. [AS1] The number that should be added to 17 to get 39 is . (A) 12 (B) 22 (C) 32 (D) 2 2. [AS3] 23 + 39 = 62 ∈ W. This is called the property with respect to addition. (A) Closure (B) Commutative (C) Associative (D) Distributive EXERCISE 2.2. PROPERTIES OF WHOLE NUMBERS 23

3. [AS3] (12 + 19) + 27 = 12 + (19 + 27) is called the property w.r.t addition. (A) Closure (B) Commutative (C) Associative (D) Distributive 4. [AS3] 42 × 79 = 79 × 42 is called the property with respect to multiplication. (A) Closure (B) Commutative (D) Distributive (C) Associative . 5. [AS3] 16 × 7 + 16 × 19 = (B) 23 × 35 (D)16 × (7 + 19) (A) 112 + 304 (C)16 × 23 × 19 6. [AS2] If n is a whole number such that n + n = n, then the value of n is . (A) 0 (B) 2 (C) 3 (D)None of these 7. [AS2] The one among the following which is not zero is . (A) 0 × 0 (B) 0 2 (C) 6−6 (D)4 ÷ 0 2 8. [AS2] If x + 12 = 12 + 7, then by commutativity of addition, x = . (A) 12 (B) 7 (C) 19 (D) 5 EXERCISE 2.2. PROPERTIES OF WHOLE NUMBERS 24

9. [AS4] The school canteen charges Rs. 30 for lunch and Rs. 5 for milk each day. The amount of money you spend in 3 days on these items is . (A) Rs. 100 (B) Rs.105 (C)Rs. 110 (D) Rs.120 10. [AS4] A vendor supplies 30 litres of milk to a hotel in the morning and 60 litres of milk in the evening. If the milk costs Rs.15 per litre, the amount due to the vendor per day is . (A) Rs. 1540 (B) Rs. 1620 (C) Rs.1780 (D) Rs.1350 11. [AS4] In a town, 1 out of 27 people own a car. If the total population of the town is 49626, the number of people who have cars is . (A) 1778 (B) 1674 (C) 1838 (D) 1968 Very Short Answer Type Questions [] 12 [AS1] Answer the following questions in one sentence. (i) Simplify: 123 + 416 + 525 (ii) Simplify: 841 + 264 + 125 + 106 (iii) Find 5 × 9 × 2 × 2 × 3 × 5. (iv) Find 3 × 2 × 4 × 5 × 1 × 2. 13 [AS2] State true or false. (i) The set of whole numbers is closed under addition. (ii) The set of whole numbers is closed under subtraction. [] (iii) The set of whole numbers is closed under multiplication. [] (iv) The set of whole numbers is not closed under division. [] (v) All natural numbers are whole numbers. [] EXERCISE 2.2. PROPERTIES OF WHOLE NUMBERS 25

14 [AS3] Fill in the blanks. (i) 12 ÷ 0 = . (ii) 0 ÷ 12 = . (iii) The additive identity in the set of whole numbers is . . (iv) The multiplicative identity in the set of whole numbers is (v) 29 × 30 = 30 × 29 .This property is called the . 15 [AS3] Fill in the blanks. (i) 5638 + 2793 = 2793 + 5638 is the property of addition. (ii) 689 × 324 = × 689 property of addition. . (iii) a + b = b + a is an example for the (iv) 0 –1 shows that subtraction of whole numbers is (v) Multiplication of whole numbers is by the example, 251 × 623 = 623 × 251. 16 [AS3] Fill in the blanks. property of . (i) (8 × 14) × 529 = 8 × (14 × 529) is an example for the multiplication. (ii) Associative property does not hold for (iii) (54 + 89) + (152) = 54 + . (iv) If a, b and c are whole numbers, then (a × b) × c = . (v) 34 × (53 × 82) = (34 × 53)× . 17 [AS3] Fill in the blanks. . (i) 37 × 19 = 37 × 10 + 37 × 5 + 37 × 4. (ii) (27 × 4) + (n × 6) = 27 (4 + 6) , then n = EXERCISE 2.2. PROPERTIES OF WHOLE NUMBERS 26

(iii) 928 × 857 = (900 + 20 + 8) × . [AS3] Answer the following questions in one sentence. (iv) Simplify: 32 × 25 + 25 × 40 (v) Simplify: 25 × 9 − 25 × 4 Short Answer Type Questions 18(i) [AS1] Find the product using the distributive property. 20 × 7 + 12 × 7 (ii) [AS1] Find the product by suitable arrangement. 8 × 25 × 2 19 (i) [AS2] We know that 0 × 0 = 0. Is there any other whole number such that a × a = a? Give reason. (ii) [AS2] Can you find out the predecessor of zero in whole numbers? Give reason. 20(i) [AS3] Write any two properties of whole numbers. (ii) [AS3] Write the additive identity and the multiplicative identity in the set of whole numbers. 21(i) [AS5] a) Place the predecessor of 13 on the number line. b) What number should be deducted from 13 to get 8? c) What number should be added to 9 to get 16? Long Answer Type Questions 22 [AS1] Find the product of the following by writing the numbers as the sum or difference of two numbers. (i) 985 × 105 (ii) 1008 × 95 25 [AS4] A tea stall uses 40 litres of milk in the morning and 46 litres of milk in the evening to make tea. With one litre of milk we can make 30 cups of tea and each cup of tea costs Rs 7.00. What is the income of the tea stall in a day? EXERCISE 2.2. PROPERTIES OF WHOLE NUMBERS 27

EXERCISE 2.3 PATTERN IN WHOLE NUMBERS 2.3.1 Key Concepts i. Patterns in numbers are not only interesting, but are useful especially for mental calculations. They help us understand properties of numbers better. 2.3.2 Additional Questions Objective Questions 1. [AS5] The number represented by the pattern is . (A) 6 (B) 0 (C) 10 (D)None of these 2. [AS5] The number represented by the pattern is . (A) 4 . (B) 20 (C) 42 (D)None of these 3. [AS1] 111 × 111 = (B) 12321 (A) 1221 (D) 2025 (C) 2125 4. [AS2] 25 × 25 = 625; 35 × 35 = 1225; then 45 × 45 = . (A) 1625 (B) 2525 (C) 2125 (D) 2025 EXERCISE 2.3. PATTERN IN WHOLE NUMBERS 28

5. [AS5] The number 2 can be represented in the pattern. (A) Line (B) Rectangle (C) Square (D) Triangle Long Answer Type Questions 6 [AS1] Fill in the blanks. (i) 486 × 99 = (ii) 58 × 25 = 58 × (20 + 5) = (iii) 143 × 7 × 1 =1001 143 × 7 × 2 =2002 143 × 7 × 3 = (iv) 167 × 6 × 1 = 1002 167 × 6 × 2 = 2004 167 × 6 × 3 = (v) 112 × 11 = 1232 113 × 11 = 1243 114 × 11 = 1254 115 × 11 = 7 [AS5] (i) Arrange 10 as a triangle using dots. (ii) Arrange 12 as a rectangle using dots. (iii) Write the next step in each of the following patterns. a) 1 × 8 = 8 12 × 8 = 88 + 8 123 × 8 = 888 + 88 + 8 EXERCISE 2.3. PATTERN IN WHOLE NUMBERS 29

b) 1 × 9 + 1 = 10 12 × 9 + 2 = 110 123 × 9 + 3 = 1110 EXERCISE 2.3. PATTERN IN WHOLE NUMBERS 30

CHAPTER 3 PLAYING WITH NUMBERS EXERCISE 3.1 DIVISIBILITY RULE 3.1.1 Key Concepts i. A number is divisible by 2 if it has one of the digits 0, 2, 4, 6 or 8 in its ones place. ii. If the sum of the digits is a multiple of 3, then the number is divisible by 3. iii. If a number is divisible by both 2 and 3, then it is also divisible by 6. iv. A number is divisible by 9, if the sum of the digits of the number is divisible by 9. v. A number is divisible by 5, if it has 0 or 5 in its ones place. vi. A number is divisible by 10, if it has 0 in its ones place. 3.1.2 Additional Questions Objective Questions . (B) 8009 1. [AS3] The number which is divisible by 2 is (A) 3472 (C) 94321 (D)None of these 2. [AS3] The number which is not divisible by 3 is . (A) 147526 (B) 73683 (C) 943218 (D)None of these 3. [AS3] The number which is divisible by 6 is . (A) 736821 (B) 943216 (C) 147528 (D)None of these EXERCISE 3.1. DIVISIBILITY RULE 31

4. [AS3] The number divisible by 10 but not divisible by 5 is . (A) 91320 (B) 91325 (C) 91000 (D)Does not exist 5. [AS3] The number 76435 is divisible by 10 if it is multiplied by . (A) 2 (B) 3 (C)5 (D)None of these 6. [AS2] If 1a548 is divisible by 3, then the value of 'a' is . (A) 0 (B) 2 (C) 7 (D) 5 Very Short Answer Type Questions 7 Choose the correct answer. (i) [AS3] 285972 is divisible by 10, when it is multiplied by . (A) 2 (B) 4 (C) 5 (D) 8 (ii) [AS2] 142315 is divisible by 10, when a number ‘A’ is added to it. The value of A is . (A) 2 (B) 3 (C) 4 (D) 5 (iii) [AS2] The digit that is to be subtracted from 523458 to make it divisible by 10 is . (A) 3 (B) 8 (C) 2 (D) 5 (iv) [AS2] 325 is multiplied by to be divisible by 10. (A) 25 (B) 52 (C) 325 (D) 125 EXERCISE 3.1. DIVISIBILITY RULE 32

(v) [AS3] The number which is divisible by 10 is . (A) 83190 (B) 235812 (C) 100002 (D) 91235 8 Choose the correct answer. . (B) 5976 (i) [AS3] The number which is divisible by 5 is (A) 3857 (C) 9765 (D) 30008 (ii) [AS3] The number which is divisible by10 is . (A) 58230 (B) 58023 (C) 80235 (D) 80325 (iii) [AS3] The number which is divisible by 5 but not by 10 is . (A) 58230 (B) 85320 (C) 80235 (D) 80532 (iv) [AS3] The number which is divisible by both 5 and 10 is . (A) 2385 (B) 6870 (C) 45875 (D) 3275 9 [AS2] Answer the following questions in one sentence. (i) If the number 2345a60b is exactly divisible by 3 and 5 then what is the maximum value of a + b? (ii) If 37610b2 is exactly divisible by 9 then what is the least value of 'b'? (iii) If 5K2 is a three digit number and it is divisible by 6 then what is the a least value of K? (iv) The product of three consecutive numbers is always divisible 6. Verify this statement with the help of 2 examples. Short Answer Type Questions 10(i) [AS2] Show that the number 68370 is divisible by 6. (ii) [AS2] Check which of the following numbers are divisible by 6. a) 726352 b) 312792 EXERCISE 3.1. DIVISIBILITY RULE 33

11(i) [AS2] 9 does not divide 12345. Justify. (ii) [AS2] Write all the three–digit numbers that can be formed using the digits 3, 4 and 5 without repetition. How many are divisible by 9? Why? 12(i) [AS2] Check whether 8543620 is divisible by 2, 3, 4 and 6 or not. (ii) [AS2] Check the divisibility of 132900460 by 2, 3, 5, 6, 9 and 10. 13(i) [AS3] Which of the following numbers is exactly divisible by 5? a) 35485 b) 423059 . (ii) [AS3] a) If a number is divisible by both 3 and 5, then it must necessarily be divisible by b) The number 7120 is divisible by . (A) 6 (B) 3 (C) 5 (D) 9 c) Which of the following numbers is divisible by 5? (A) 3189 (B) 20053 (C) 50230 (D) 55081 14 (i) a) [AS3] If a number is divisible by 5 and 8, then it is necessarily divisible by . b) If a number is is divisible by 2 and 3, then it is necessarily divisible by . (ii) [AS3] . a) The number 15938a is divisible by 6, then the least value of a is b) 9p8071 is divisible by 11. The least possible value of p is . c) A number is divisible by 4 and 3, but not by 24. The number is . EXERCISE 3.1. DIVISIBILITY RULE 34

Long Answer Type Questions 15 [AS1] Form the greatest 5–digit number using the digits 6, 4, 9, 2 and 8. Find the least number to be subtracted from it so that the resulting number is divisible by 3. 16 [AS4] 18 is divisible by both 2 and 3. It is also divisible by 2 × 3 = 6. Similarly, a number is divisible by both 4 and 6. Can we say that the number is also divisible by 4 × 6 = 24? If not, give an example to justify your answer. EXERCISE 3.1. DIVISIBILITY RULE 35

EXERCISE 3.2 FACTORS 3.2.1 Key Concepts i. Factor: A number which divides the other number exactly is called a factor of that number. Ex: 1, 2, 3, 4, 6, 12 are the factors of 12. ii. The number 1 is a factor of every number and is the smallest of all factors. iii. Every number is a factor of itself and is the greatest of its factors. iv. Prime numbers: The numbers whose only factors are 1 and the number itself are called prime numbers. Ex: 2, 3, 5, 7, 11, 13 and so on. v. Composite numbers: Numbers having more than two factors are called composite numbers. Ex: 4, 6, 8, 9 and so on. vi. The number 1 has only one factor (i.e., itself) . So, 1 is neither prime nor composite. vii. Co–prime number: Two numbers with only 1 as common factor are called co–primes or relatively prime. Ex: 2 and 3; 7 and 8. viii. Twin primes: Twin primes are prime numbers that differ from each other by two. Ex:(3, 5); (5, 7); (11, 13); (17, 19); (41, 43)etc. ix. Common factors: Common factors are those numbers which are factors of all the given numbers. Ex: The factors of 6 are 1, 2, 3, 6 and the factors of 12 are 1, 2, 3, 4, 6, 12 ∴ The common factors of 6 and 12 are 1, 2, 3, 6. 3.2.2 Additional Questions Objective Questions 1. [AS3] The least factor of every number is . (A) 0 (B) 1 (C) 2 (D) 3 2. [AS3] The least prime number is . (A) 0 (B) 1 (C) 2 (D) 3 EXERCISE 3.2. FACTORS 36

3. [AS3] The least composite number which is odd is . (A) 0 (B) 4 (C) 5 (D) 9 4. [AS3] A pair of co–primes is . (A) (24, 77) (B) (24, 36) (C)(17, 51) (D)None of these 5. [AS3] A pair of twin primes is . (A) (3, 13) (B) (17, 19) (C)(23, 29) (D)(31, 37) Very Short Answer Type Questions 6 [AS3] Fill in the blanks. (i) Number of factors for 37 is . (ii) Every factor is less than or equal to the . . (iii) Every number is of itself. (iv) is a factor of all natural numbers. (v) The factors of 28 are 7 [AS3] Answer the following questions in one sentence. (i) What is the smallest prime number? (ii) Which is the only even prime number? (iii) What is the greatest prime number between 5 and 20? (iv) Write two prime numbers whose product is 119. (v) Write the number which is neither prime nor composite. 8 [AS3] Answer the following questions in one sentence. (i) List the composite numbers between 20 and 30. (ii) The smallest composite number is . EXERCISE 3.2. FACTORS 37

(iii) The smallest odd composite number is . (iv) The greatest single–digit composite number is . (v) The only even number which is not a composite number is . 9 [AS3] Choose the correct answer. (i) Pairs of primes, that have a difference of two are called . (A) Twin primes (B) Co–primes (C)Composite numbers (D)None of these (ii) A pair of twin primes is . (A) (2, 5) (B) (3, 7) (C)(7, 9) (D)(5, 7) (iii) A pair of twin primes between 40 and 60 is . (A) (41, 45) (B) (43, 45) (C)(41, 43) (D)(45, 47) (iv) The missing number in the pair of twin primes ( , 73) is . (A) 75 (B) 77 (C) 71 (D) 74 (v) The numbers in the pair (25, 27) are . (A) Twin primes (B) Not twin primes (C) Primes (D)None of these EXERCISE 3.2. FACTORS 38

EXERCISE 3.3 PRIME FACTORIZATION 3.3.1 Key Concepts i. When a number is expressed as a product of its factors, we say that the number has been factorized. The process of finding the factors is called factorization. ii. Factorization of a number in which all the factors are prime numbers, is known as prime factorization. 3.3.2 Additional Questions Objective Questions 1. [AS3] Expressing a given number as the product of prime numbers is called . (A) Factorization (B) Prime factorization (C) Division (D)None of these 2. [AS3] 28 as the product of prime factors in exponential form is . (A) 2 × 2 × 7 (B) 22 × 7 (C)4 × 7 (D)1 × 28 3. [AS1] The missing factor in the factor tree of 72 is . (A) 2 (B) 9 (C) 3 (D) 4 EXERCISE 3.3. PRIME FACTORIZATION 39

4. [AS1] The missing factor in the factorization of 750 by division method is . (A) 125 (B) 75 (C) 105 (D)None of these . 5. [AS3] The prime factorization of 216 is (A) 6 × 36 (B) 12 × 18 (C)2 × 108 (D)2 × 2 × 2 × 3 × 3 × 3 Very Short Answer Type Questions 6 [AS2] Answer the following questions in one sentence. I am the smallest number, having four different prime factors. Can you find me? Short Answer Type Questions 7(i) [AS1] a) Find the prime factors of 2520 using the division method. b) Factorize the largest 4–digit number. c) Factorize the smallest 4–digit number. (ii) [AS1] Factorize 884 using the division method and express as a product of prime factors. 8(i) [AS1] a) Draw a factor tree of 360. b) Write the missing numbers in the factor tree of 90. EXERCISE 3.3. PRIME FACTORIZATION 40

(ii) [AS1] Draw the factor tree of 48. 9(i) [AS1] Factorize a) 360 b) 1284 by the division method and express them as a product of prime factors in exponential form. (ii) [AS1] Factorize the following using factor tree method and also write them as product of prime factors in exponential form. a) 1890 b) 3456 EXERCISE 3.3. PRIME FACTORIZATION 41

EXERCISE 3.4 COMMON FACTORS 3.4.1 Key Concepts i. Highest Common Factor (HCF): The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors. It is also called the Greatest Common Divisor (GCD). ii. Least Common Multiple (LCM): The Least Common Multiple of two or more given numbers is the lowest (or smallest or least) of their common multiples. iii. Relationship between LCM and HCF: Product of LCM and HCF = Product of the two numbers. 3.4.2 Additional Questions Objective Questions . (B) 3 1. [AS3] The common prime factor of 24 and 56 is (A) 2 (C)7 (D)None of these 2. [AS1] The HCF of 24 and 56 is . (A) 2 (B) 4 (C) 8 (D)None of these 3. [AS3] The HCF of two co–prime numbers is . (A) 0 (B) 1 (C)The product of the two numbers (D)None of these 4. [AS1] The HCF of 36 and 49 is . (A) 36 (B) 49 (C)36 × 49 (D) 1 EXERCISE 3.4. COMMON FACTORS 42

5. [AS1] The HCF of 64 and 360 is . (A) 2 (B) 3 (C) 8 (D) 6 Very Short Answer Type Questions 6 [AS1] Fill in the blanks. (i) The HCF of 90 and 60 is . (ii) The HCF of 28, 32 and 26 is . (iii) The HCF of 52, 65, 91 is . (iv) The HCF of 28, 35 and 49 is . [AS3] Answer the following questions in one sentence. (v) Find the HCF of 80 and 56. Short Answer Type Questions 7(i) [AS1] Find the HCF of a) 84 and 90 b) 255 and 357 (ii) [AS1] Find the HCF of a) 391 and 425 b) 36 and 48 8(i) [AS1] Find the HCF of a) 18 and 27 b) 106 and 159 (ii) [AS1] Find the HCF of a) 32 and 128 b) 504 and 792 EXERCISE 3.4. COMMON FACTORS 43

9 [AS1] Find the greatest number that divides 47, 67 and 107 leaving a remainder 7. 10(i) [AS4] Renu purchases two bags of fertilisers weighing 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertiliser an exact number of times. (ii) [AS4] Three petrol tankers have 2800 l , 4200 l and 5740 l. Find the maximum capacity of a container which can measure the petrol of all the three tankers when used an exact number of times. 11 [AS4] The length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm respectively. Determine the longest tape which can measure the three dimensions of the room exactly. Long Answer Type Questions 12 [AS1] Find the HCF of the following numbers : (i) 10, 35 and 40 (ii) 72, 120 and 192 13 [AS1] Find the HCF of the following numbers by the continued division method: (i) 2261, 3059 and 3325 (ii) 101, 573 and 1079 14 [AS4] Two cans contain 60 litres and 135 litres of milk respectively. Find a can of maximum capacity which can measure the milk in both the cans an exact number of times. 15 [AS4] The areas of floors of three rooms are 184 sq.ft., 212 sq.ft. and 232 sq.ft. Find the maximum size of the tiles to get the flooring covered with an exact number of tiles. EXERCISE 3.4. COMMON FACTORS 44

EXERCISE 3.5 COMMON MULTIPLES 3.5.1 Key Concepts i. Least Common Multiple (LCM) : The Least Common Multiple of two or more given numbers is the lowest (or smallest or least) of their common multiples. 3.5.2 Additional Questions Objective Questions 1. [AS3] The common multiple of two co–prime numbers is . (A) 1 (B) Their product (C)Their quotient (D)None of these 2. [AS1] One of the common multiples of 15 and 20 is . (A) 5 (B) 30 (C) 120 (D) 150 3. [AS1] The LCM of 12 and 20 is . (A) 60 (B) 30 (C) 120 (D) 180 4. [AS1] The LCM of 35 and 49 is . (A) 980 (B) 735 (C) 490 (D) 245 5. [AS1] One of the common multiples of 1 and 80 is . (A) 1 (B) 80 (C) 40 (D) 120 EXERCISE 3.5. COMMON MULTIPLES 45

Short Answer Type Questions 6(i) [AS1] Find the LCM of the given numbers by prime factorization: a) 112, 252 and 99 b) 8, 16, 24 and 32 (ii) [AS1] Find the LCM of the given numbers 216, 144 and 360 by prime factorization. 7(i) [AS1] Find the LCM of 25, 40 and 60. (ii) [AS1] a) Find the LCM of 36, 75 and 80. b) Find the LCM of 64, 96 and 112. 8 [AS1] Find the smallest number which is 8 less than a common multiple of 57, 76 and 90. 9 [AS4] What is the least number of toffees to be bought, so that they can be distributed equally among 15, 30 and 45 students? EXERCISE 3.5. COMMON MULTIPLES 46

EXERCISE 3.6 RELATIONSHIP BETWEEN LCM AND HCF 3.6.1 Key Concepts i. Relationship between LCM and HCF: Product of LCM and HCF = Product of the two numbers. 3.6.2 Additional Questions Objective Questions 1. [AS3] The LCM of two numbers is their product. Then their HCF is . (A) 1 (B) 0 (C)Product of the numbers (D)None of these 2. [AS3] Product of two numbers = Their LCM × . (A) Quotient (B) 1 (C) H.C.F (D)None of these 3. [AS1] The LCM of 24 and 36 is 72. Then their HCF is . (A) 2 (B) 3 (C) 6 (D) 12 4. [AS1] The HCF of 25 and 80 is 5. Then their LCM is . (A) 200 (B) 400 (C) 600 (D) 800 5. [AS1] The LCM and HCF of two numbers are 80 and 8. If one of the numbers is 16 then the other number is . (A) 640 (B) 320 (C) 40 (D) 1280 EXERCISE 3.6. RELATIONSHIP BETWEEN LCM AND HCF 47