# Factors and Multiples - Class 5 - Mathematics

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## Exercise 17 - Factors and Multiples | R.S. Aggarwal | Mathematics | Class 5

Write the first six multiples of:

(a) 6

(b) 11

(c) 19

(d) 21

(e) 25

Here are the first six multiples for each number requested:

(a) The first six multiples of **6** are 6, 12, 18, 24, 30, 36.

(b) The first six multiples of **11** are 11, 22, 33, 44, 55, 66.

(c) The first six multiples of **19** are 19, 38, 57, 76, 95, 114.

(d) The first six multiples of **21** are 21, 42, 63, 84, 105, 126.

(e) The first six multiples of **25** are 25, 50, 75, 100, 125, 150.

Write all the factors of each of the following numbers.

(a) 18

(b) 28

(c) 32

(d) 45

(e) 60

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Sign up nowWhich of the following numbers are divisible by 2 ?

(a) 976

(b) 670

(c) 843

(d) 5694

(e) 7358

(f) 2890

(g) 1985

(h) 299

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Sign up nowWhich of the following numbers are divisible by 3 ?

(a) 837

(b) 1493

(c) 26412

(d) 37401

(e) 16339

(f) 23571

(g) 42105

(h) 31547

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Sign up nowWhich of the following numbers are divisible by 4 ?

(a) 894

(b) 1056

(c) 2360

(d) 7130

(e) 16338

(f) 69704

(g) 24842

(h) 97312

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Which of the following numbers are divisible by 5 ?

(a) 1980

(b) 1785

(c) 3206

(e) 2730

(f) 6309

(g) 9915

(d) 27905

(h) 3617

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Which of the following numbers are divisible by 6 ?

(a) 3132

(b) 5704

(c) 8316

(d) 9430

(e) 7038

(f) 17703

(g) 7812

(h) 8721

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Which of the following numbers are divisible by 7 ?

(a) 252

(b) 1204

(c) 5843

(d) 8036

(e) 9308

(f) 3045

(g) 7833

(h) 5233

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Which of the following numbers are divisible by 8 ?

(a) 1372

(b) 10568

(c) 62156

(d) 50432

(e) 73152

(f) 796504

(g) 59238

(h) 279136

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Which of the following numbers are divisible by 9 ?

(a) 8316

(b) 7509

(c) 4186

(d) 26901

(e) 50553

(f) 12501

(g) 3499

(h) 20367

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Which of the following numbers are divisible by 10 ?

(a) 1155

(b) 2960

(c) 8740

(d) 2068

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Which of the following numbers are divisible by 11 ?

(a) 2101

(b) 32571

(c) 35064

(d) 20833

(e) 17622

(f) 58564

(g) 101011

(h) 202202

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Separate even and odd numbers from the following.

(a) 23

(b) 36

(c) 41

(d) 87

(e) 60

(f) 74

(g) 258

(h) 605

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Write all even numbers between

(a) 73 and 87

(b) 519 and 531

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Write all odd numbers between

(a) 64 and 80

(b) 624 and 640

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## Exercise 18 - Factors and Multiples | R.S. Aggarwal | Mathematics | Class 5

Which of the following numbers are prime numbers?

$1,11,21,57,67,19,91,63,83,89$

The prime numbers from the given list are:

- $11$
- $19$
- $67$
- $83$
- $89$

The other numbers ($1$, $21$, $57$, $63$, $91$) are not prime.

Which of the following numbers are composite numbers?

$1,79,97,51,61,87,81,78,93,47$

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List all prime numbers between 1 and 50 .

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List all prime numbers between 51 and 100 .

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List all twin-primes between 1 and 50 .

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List seven consecutive composite numbers less than 100 .

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Give four examples of pairs of co-primes.

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Write the prime factorisation of each of the following numbers using division by prime numbers.

(a) 60

(b) 84

(c) 180

(d) 210

(e) 728

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Write the prime factorisation of each of the following numbers using factor tree.

(a) 90

(b) 216

(c) 300

(d) 315

(e) 450

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Give examples of 4 pairs of prime numbers which have only one composite number between them 11. Fill in the blanks.

(a) is a factor of every number.

(b) The least prime number is

(c) The smallest composite number is

(d) Each prime number has exactly factors.

(e) is neither prime nor composite.

(f) is the only even prime number.

(g) The largest 2-digit prime number is

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## Exercise 19 - Factors and Multiples | R.S. Aggarwal | Mathematics | Class 5

Find the HCF of:

(a) 16 and 24

(b) 18 and 27

(c) 32 and 40

(d) 8, 20 and 32

(e) 14, 28 and 35

(f) 16,20 and 36

The Highest Common Factor (HCF) for each pair or group of numbers is as follows:

(a) **HCF of 16 and 24:** 8

(b) **HCF of 18 and 27:** 9

(c) **HCF of 32 and 40:** 8

(d) **HCF of 8, 20, and 32:** 4

(e) **HCF of 14, 28, and 35:** 7

(f) **HCF of 16, 20, and 36:** 4

Find the HCF of the following pair of numbers by prime factorisation.

(a) 45 and 60

(b) 36 and 54

(c) 48 and 60

(d) 75 and 90

(e) 52 and 78

(f) 72 and 108

(g) 42 and 112

(h) 54 and 114

(i) 168 and 216

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Find the HCF of the following numbers, using prime factorisation.

(a) 24, 40 and 56

(b) 36,48 and 72

(c) 42,63 and 105

(d) 112, 140 and 168

(e) 144,180 and 252

(f) 91,49 and 112

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Find the HCF of the following numbers by common division method.

(a) 24 and 80

(b) 18 and 48

(c) 165 and 220

(d) 48,80 and 96

(e) 42, 70 and 112

(f) 144,180 and 192

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Find the HCF of the following numbers, using division method.

(a) 96 and 120

(b) 81 and 108

(c) 144 and 312

(d) 252 and 576

(e) 575 and 920

(f) 605 and 935

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Find the HCF of the following numbers, using division method.

(a) 60,96 and 150

(b) 75,100 and 140

(c) 270, 945 and 2175

(d) 902,1394 and 3321

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## Exercise 20 - Factors and Multiples | R.S. Aggarwal | Mathematics | Class 5

Find the LCM of the given numbers using prime factorisation method.

(a) 18,24

(b) 36,45

(c) 63,105

(d) $28,56,84$

(e) $36,54,81$

(f) $27,54,90$

Here are the Least Common Multiples (LCMs) using the prime factorization method for the given numbers:

(a) For 18 and 24: $$ LCM(18, 24) = 72 = 2^3 \cdot 3^2 $$

(b) For 36 and 45: $$ LCM(36, 45) = 180 = 2^2 \cdot 3^2 \cdot 5 $$

(c) For 63 and 105: $$ LCM(63, 105) = 315 = 3^2 \cdot 5 \cdot 7 $$

(d) For 28, 56, and 84: $$ LCM(28, 56, 84) = 168 = 2^3 \cdot 3 \cdot 7 $$

(e) For 36, 54, and 81: $$ LCM(36, 54, 81) = 324 = 2^2 \cdot 3^4 $$

(f) For 27, 54, and 90: $$ LCM(27, 54, 90) = 270 = 2 \cdot 3^3 \cdot 5 $$

These answers are derived from factoring each number into its prime factors, then taking the highest power of each prime that appears in any of the numbers, and finally combining these to get the LCM.

Find the LCM of the given numbers using short division method.

(a) 25,30

(b) 32,48

(c) 42,70

(d) $28,42,56$

(e) $75,100,150$

(f) $96,144,192$

(g) $90,135,180$

(h) $102,136,170$

(i) $64,72,96,108$

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## Exercise 21 - Factors and Multiples | R.S. Aggarwal | Mathematics | Class 5

Find the HCF and LCM of:

(a) 87 and 145

(b) 161 and 207

(c) 270 and 450

Here are the HCF (Highest Common Factor) and LCM (Least Common Multiple) for the given pairs:

(a) For 87 and 145:

HCF: 29

LCM: 435

(b) For 161 and 207:

HCF: 23

LCM: 1449

(c) For 270 and 450:

HCF: 90

LCM: 1350

The HCF of two numbers is 12 and their $L C M$ is 180 . If one of the numbers is 36 , find the other.

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The HCF of two numbers is 30 and their LCM is 2310 . If one of the numbers is 210 , find the other.

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The product of two numbers is 2925 and their HCF is 15 . Find the LCM of these numbers.

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The product of two numbers is 3750 and their $L C M$ is 150 . Find the HCF of these numbers.

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Find the largest number which divides 209 and 260 leaving remainder 5 in each case.

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Two ropes of lengths $16 \mathrm{~m}$ and $24 \mathrm{~m}$ are to be cut into small pieces of equal lengths. What will be the maximum length of each piece?

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Three drums contain respectively 36 litres, 45 litres and 72 litres of oil. Find the capacity of the large: container which can measure the content of each drum an exact number of times.

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Find the least number which is exactly divisible by each one of the numbers 12,16 and 24 .

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Find the least number of stones so that heaps of 15,20 and 30 stones can be made.

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Six bells commence tolling together and toll at intervals of $2,4,6,8,10$ and 12 seconds respectivel After how much time will they toll together again?

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## Question Bag 1 - Factors and Multiples | R.S. Aggarwal | Mathematics | Class 5

The sum of the first five multiples of 6 is

(a) 30

(b) 60

(c) 90

(d) 120

The first five multiples of 6 are 6, 12, 18, 24, and 30.

The sum of these numbers is: $$ 6 + 12 + 18 + 24 + 30 = 90 $$

Therefore, the correct option is (c) 90.

Which is the only number having only one factor?

(a) 0

(b) 1

(c) 2

(d) 3

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HCF of 36 and 84 is

(a) 4

(b) 6

(c) 12

(d) 18

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## Question Bag 2 - Factors and Multiples | R.S. Aggarwal | Mathematics | Class 5

Circle the prime numbers.

39 | 51 | 19 | 71 | 27 | 59 | 73 | 55 | 91 | 67 | 83 | 97 | 15 | 43 |
---|

The prime numbers from the given list are:

19

71

59

73

67

83

97

43

Check the divisibility of each of the following numbers by $2,3,4,5,6,7,8,9,10$ and 11. Put a ✅ for 'divisible' and a ❌ for 'not divisible'.

Number | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 10 | 11 | |
---|---|---|---|---|---|---|---|---|---|---|

(a) | 99880 | |||||||||

(b) | 46632 | |||||||||

© | 67968 | |||||||||

(d) | 726354 | |||||||||

(e) | 50505 |