Table of Contents

Toggle## Class 6, Maths, Chapter 3, Exercise 3.4 Solutions

**Q.1. Find the common factors of :**

**(a) 20 and 28 **

**(b) 15 and 25 **

**(c) 35 and 50 **

**(d) 56 and 120**

**Ans:**

**(a) 20 and 28**

To find the common factors of 20 and 28, we can list the factors of each number and find the ones they have in common.

The factors of 20 are: 1, 2, 4, 5, 10, 20.

The factors of 28 are: 1, 2, 4, 7, 14, 28.

The common factors of 20 and 28 are the ones they both have in common, which are: 1, 2, and 4.

Therefore, the common factors of 20 and 28 are 1, 2, and 4.

**In other words: **

Factors of 20 = 1, 2, 4, 5, 10, 20

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

Common factors = 1, 2, 4

**(b) 15 and 25**

Factors of 15 = 1, 3, 5, 15

Factors of 25 = 1, 5, 25

Common factors = 1, 5

**(c) 35 and 50**

Factors of 35 = 1, 5, 7, 35

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

Common factors = 1, 5

** **

**(d) 56 and 120**

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

**Q.2. Find the common factors of :**

**(a) 4, 8 and 12 **

**(b) 5, 15 and 25**

**Ans:**

**(a) 4, 8 and 12**

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) 5, 15 and 25**

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

**Q.3. Find first three common multiples of :**

**(a) 6 and 8 **

**(b) 12 and 18**

**Ans:**

**(a) 6 and 8 **

Multiple of 6 = 6, 12, 18, 24, 30, 36, 42, 48,54, 60,72, ………..

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

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

**(b) 12 and 18**

Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ………….

Multiple of 18 = 18, 36, 54, 72, 90, 108, 126………

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

**Q.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**

**Ans:**

**Co -prime:** Two numbers are said to be co-prime if they don’t have any common factor other than 1

**(a) 18 and 35**

Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 35 = 1, 5, 7, 35

Common factor = 1

Since, their common factor is 1. Hence, they are co-prime numbers.

**(b) 15 and 37**

Factors of 15 = 1, 3, 5, 15

Factors of 37 = 1, 37

Common factors = 1

Since, their common factor is 1. Hence, they are **co-prime** numbers.

**(c) 30 and 415**

Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

Factors of 415 = 1, 5, 83, 415

Common factors = 1, 5

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

**(d) 17 and 68**

Factors of 17 = 1, 17

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

Common factors = 1, 17

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

**(e) 216 and 215**

Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

Factors of 215 = 1, 5, 43, 215

Common factors = 1

Since, their common factor is 1. Hence, they are **co-prime numbers.**

**(f) 81 and 16**

Factors of 81 = 1, 3, 9, 27, 81

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

Common factors = 1

Since, their common factor is 1. Hence, they are **co-prime numbers.**

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

**Ans:**

Multiple of 5 = 5,10,15,20,25,30,35,40,45,50,55,**60**….

Multiple of 12 = 12,24,36,48,**60**….

Answer: Common factor is 60.

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

**Ans: **

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

Since, the number is divisible by 12. Hence, it also divisible by its factors i.e. 1, 2, 3, 4, 6

## NCERT Solutions For Class 6 Maths, Chapter 3 Playing With Numbers (All Exercises)

**Class 6, Maths, Chapter 3, Playing With Numbers **

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.1**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.2**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.3**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.4** **← You are here**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.5**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.6**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.7**