# Here we have given NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4.

- Playing with Numbers Class 6 Ex 3.1
- Playing with Numbers Class 6 Ex 3.2
- Playing with Numbers Class 6 Ex 3.3
- Playing with Numbers Class 6 Ex 3.5
- Playing with Numbers Class 6 Ex 3.6
- Playing with Numbers Class 6 Ex 3.7

Board | CBSE |

Textbook | NCERT |

Class | Class 6 |

Subject | Maths |

Chapter | Chapter 3 |

Chapter Name | Playing with Numbers |

Exercise | Ex 3.4 |

Number of Questions Solved | 7 |

Category | NCERT Solutions |

## NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4

Ex 3.4 Class 6 Maths Question 1.

Find the common factors of:

(a) 20 and 28

(b) 15 and 25

(c) 35 and 50

(d) 56 and 120

Solution:

(a) We have, 20 = 1 x 20

= 2 x 10

= 4 x 5

∴ All the factors of 20 are 1, 2, 4, 5, 10 and 20

Again, 28 = 1 x 28

28 = 2 x 14

28 = 4 x 7

∴ All the factors of 28 are 1, 2, 4, 7, 14 and 28.

Out of these 1, 2 and 4 occur in both the lists.

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

(b) We have, 15 = 1 x 15

15 = 3 x 5

∴ All the factors of 15 are 1, 3, 5 and 15.

Again, 25 = 1 x 25

25 = 5 x 5

∴ All the factors of 25 are 1, 5 and 25.

Out of these 1 and 5 occur in both the lists.

∴1 and 5 are common factors of 15 and 25.

(c) We have, 35 = 1 x 35

35 = 5 x 7

∴ All the factors of 35 are 1, 5, 7 and 35.

Again, 50 = 1 x 50

50 = 2 x 25

50 = 5 x 10

∴ All the factors of 50 are 1, 2, 5, 10, 25 and 50. ,

Out of these 1 and 5 occur in both the lists.

∴ 1 and 5 are common factors of 35 and 50.

(d) We have, 56 = 1 x 56

56 = 2 x 28

56 = 4 x 14

56 = 7 x 8

∴ All the factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.

Again, 120 = 1 x 120

120 = 2 x 60

120 = 3 x 40

120 = 4 x 30

120 = 5 x 24

120 = 6 x 20

120 = 8 x 15

120 = 10 x 12

∴ All the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

Out of these 1, 2, 4 and 8 occur in both the lists.

∴ 1, 2, 4 and 8 are common factors of 56 and 120.

Ex 3.4 Class 6 Maths Question 2.

Find the common factors of:

(a) 4, 8 and 12

(b) 5, 15 and 25

Solution:

(a) We have, 4=1 x 4

4 = 2 x 2

∴ All the factors of 4 are 1, 2 and 4.

Again, 8 = 1 x 8

8 = 2 x 4

∴All the factors of 8 are 1, 2, 4 and 8.

Again, 12 = 1 x 12

12 = 2 x 6

12 = 3 x 4

∴ All the factors of 12 are 1, 2, 3, 4, 6 and 12.

Out of these 1, 2 and 4 occur in all the three lists.

∴ 1, 2 and 4 are common factors of 4, 8 and 12.

(b) We have, 5 = 1 x 5

∴All the factors of 5 are 1 and 5.

15 = 1 x 15

15 = 3 x 5

∴ All the factors of 15 are 1, 3, 5 and 15.

25 = 1 x 25

25 = 5 x 5

∴ All the factors of 25 are 1, 5 and 25.

Out of these 1 and 5 occur in all the three lists.

∴ 1 and 5 are common factors of 5, 15 and 25.

Ex 3.4 Class 6 Maths Question 3.

Find first three common multiples of:

(a) 6 and 8

(b) 12 and 18

Solution:

(a) Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72,…

Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72,…

Out of these 24, 48, 72, … occur in both thfe lists.

∴ The first three common multiples of 6 and’8 are 24, 48 and 72.

(b) Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, …

Multiples of 18 are 18, 36, 54, 72, 90, 108, …

Out of these 36, 72, 108, … occur in both the lists.

∴ The first three common multiples of 12 and 18 are 36, 72 and 108.

Ex 3.4 Class 6 Maths Question 4.

Write all the numbers less than 100 which are corrimon multiples of 3 and 4.

Solution:

Common multiples of 3 and 4 are multiples of 3 x 4 i. e., 12.

∴ Common multiples of 3 and 4 less than 100 are 12, 24, 36,48, 60, 72, 84 and 96.

Ex 3.4 Class 6 Maths 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

Solution:

(a) Factors of 18 are 1, 2, 3, 6, 9 and 18 and, that of 35 are 1, 5, 7 and 35.

∴ Common factor of 18 and 35 is 1.

Thus, 18 and 35 are co-prime.

(b) Factors of 15 are 1, 3, 5 and 15 and, that of 37 are 1 and 37.

∴ Common factor of 15 and 37 is 1.

Thus, 15 and 37 are co-prime.

(c) Since 5 is a common factor of 30 and 415.

∴ 30 and 415 are not co-prime.

(d) ∴ 68 + 17 = 4 i.e., 17 is a common factor of 17 and 68.

∴ 17 and 68 are not co-prime.

(e) Since 1 is the only common factor of 216 and 215.

∴ 216 and 215 are co-prime.

(f) Since 1 is the only common factor of 81 and 16.

∴ 81 and 16 are co-prime.

Ex 3.4 Class 6 Maths Question 6.

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

Solution:

Since a number is divisible by both 5 and 12.

So, it is also divisible by 5 x 12 i. e., 60.

Ex 3.4 Class 6 Maths Question 7.

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

Solution:

Factors of 12 are 1, 2, 3, 4 and 12.

Since a number is divisible by 12. So, it is also divisible by the factors of 12.

Thus, the number is also divisible by 2, 3 and 4.

We hope the NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4, drop a comment below and we will get back to you at the earliest.

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