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Home » NCERT Solutions » Class 6 » Maths » Chapter 3 Playing with Numbers » Exercise 3.4

Exercise 3.4

Last Updated on July 3, 2023 By Mrs Shilpi Nagpal

Class 6 Mathematics Chapter 3|
Playing with Numbers | Exercise 3.4

Question 1: Find the common factors of:

(a) 20 and 28

(b) 15 and 25

(c) 35 and 50

(d) 56 and 120

Answer 1: (a) Factors of 20 = 1, 2, 4, 5, 10, 20

Factors of 28 = 1, 2, 4, 7, 14, 28

Common factors = 1, 2, 4

(b) Factors of 15 = 1, 3, 5, 15

Factors of 25 = 1, 5, 25

Common factors = 1, 5

(c) Factors of 35 = 1, 5, 7, 35

Factors of 50 = 1, 2, 5, 10, 25, 50

Common factors = 1, 5

(d) Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56

Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 60, 120

Common factors = 1, 2, 4, 8

Question 2: Find the common factors of:

(a) 4, 8 and 12

(b) 5, 15 and 25

Answer 2: (a) Factors of 4 = 1, 2, 4

Factors of 8 = 1, 2, 4, 8

Factors of 12 = 1, 2, 3, 4, 6, 12

Common factors of 4,8 and 12 = 1, 2, 4

(b) Factors of 5 = 1, 5

Factors of 15 = 1, 3, 5,15

Factors of 25 = 1, 5,25

Common factors of 5, 15 and 25 = 1, 5

Question 3: Find the first three common multiples of:

(a) 6 and 8

(b) 12 and 18

Answer 3: (a) Multiple of 6 = 6, 12, 18, 24, 30, 36, 42, 28, 54, 60, 72, …………

Multiple of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, …………………….

Common multiples of 6 and 8 = 24, 48, 72

(b) Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ………

Multiple of 18 = 18, 36, 54, 72, 90, 108, ………………………………

Common multiples of 12 and 18 = 36, 72, 108

Question 4: Write all the numbers less than 100 which are common multiples of 3 and 4.

Answer 4: Multiple of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99

Multiple of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100

Common multiples of 3 and 4 = 12, 24, 36, 48, 60, 72, 84, 96

Question 5: Which of the following numbers are co-prime:

(a) 18 and 35

(b) 15 and 37

(c) 30 and 415

(d) 17 and 68

(e) 216 and 215

(f) 81 and 16

Answer 5: (a) Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 35 = 1, 5, 7, 35

Common factor = 1

Since, both have only one common factor, i.e., 1, therefore, they are co-prime numbers.

(b) Factors of 15 = 1, 3, 5, 15

Factors of 37 = 1, 37

Common factor = 1

Since, both have only one common factor, i.e., 1, therefore, they are co-prime numbers.

(c) Factors of 30 = 1, 2, 3, 5, 6, 15, 30

Factors of 415 = 1, 5, …….., 83, 415

Common factor = 1, 5

Since, both have more than one common factor, therefore, they are not co-prime numbers.

(d) Factors of 17 = 1, 17

Factors of 68 = 1, 2, 4, 17, 34, 86

Common factor = 1, 17

Since, both have more than one common factor, therefore, they are not co-prime numbers.

(e) Factors of 216 = 1, 2, 3, 4, 6, 8, 36, 72, 108, 216

Factors of 215 = 1, 5, 43, 215

Common factor = 1

Since, both have only one common factor, i.e., 1, therefore, they are co-prime numbers.

(f) Factors of 81 = 1, 3, 9, 27, 81

Factors of 16 = 1, 2, 4, 8, 16

Common factor = 1

Since, both have only one common factor, i.e., 1, therefore, they are co-prime numbers.

Question 6: A number is divisible by both 5 and 12. By which other number will that number be always divisible?

Answer 6: 5 x 12 = 60.

The number must be divisible by 60.

Question 7: A number is divisible by 12. By what other numbers will that number be divisible?

Answer 7: Factors of 12 are 1, 2, 3, 4, 6 and 12.

Therefore, the number also be divisible by 1, 2, 3 4 and 6.

Filed Under: Chapter 3 Playing with Numbers, Class 6, Maths, NCERT Solutions

About Mrs Shilpi Nagpal

Author of this website, Mrs. Shilpi Nagpal is MSc (Hons, Chemistry) and BSc (Hons, Chemistry) from Delhi University, B.Ed. (I. P. University) and has many years of experience in teaching. She has started this educational website with the mindset of spreading free education to everyone.

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  1. Deerghayu says

    May 25, 2020 at 7:48 pm

    Good

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