Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 3 Playing With Numbers Ex 3.4 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 6 Maths Chapter 3 Playing With Numbers Ex 3.4

Question 1.

Find the common factors oft

(a) 20 and 28

(b) 15 and 25

(c) 35 and 50

(d) 56 and 120

Solution:

(a) 20 and 28

Wehave: 20 = 1 x 20

20 = 2 x 10

20 = 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 = 7 x 4

AIl the factors of 28 are: 1, 2, 4, 7, 14 and 28 . . .(ii)

From

(i) and

(ii), common factors of 20 and 28 are : 1, 2 and 4.

(b) 15 and 25

Since 15 = 1 x 15

15 = 3 x 5

All the factors of 15 are : 1, 3, 5 and 15 …(i)

Again, 25 = 1 x 25

25 = 5 x 5

All the factors of 25 are: 1, 5 and 25 …(ii)

From

(i) and

(ii), common factors of 15 and 25 are : 1 and 5.

(c) 35 and 50

Since 35 = 1 x 35

35 = 5 x 7

All the factors of 35 are: 1, 5, 7 and 35 ……..(i)

Again, 50 = I x 50

50 = 2 x 25

50 = 5 x 10

All the factors of 50 are: 1, 2, 5, 10, 25, 50 …(ii)

From

(i) and

(ii), common factors of 35 and 50 are : 1 and 5.

(d) 56 and 120

Since 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

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

Question 2.

Find the common factors of

(a) 4, 8 and 12

(b) 5, 15 and 25

Solution:

(a) 4, 8 and 12

Factors of 4 are : 1, 2 and 4

Factors of 8 are : 1, 2, 4 and 8

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

Common factors of 4, 8 and 12 are: 1, 2 and 4.

(b) 5, 15 and 25

Factors of 5 are : 1 and 5

Factors of 15 are : 1, 3, 5 and 15

Factors of 25 are : 1, 5 and 25

Common factors of 5, 15 and 25 are : 1 and 5.

Question 3.

Find first three common multiples oft

(a) 6 and 8

(b) 12 and 18

Solution:

(a) 6 and 8

Since multiples of 6 are :

Multiples of 8 are :

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

(b) 12 and 18

Since, multiples of 12 are:

Multiples of 18 are :

First three common multiples of 12 and 18 are : 36, 72 and 108.

Question 4.

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

Solution:

Multiples of 3, which are less than 100, are :

Multiples of 4, which are less than 100, are :

Common multiples of 3 and 4, which are less than 100, are :

12, 24, 36, 48, 60, 72, 84 and 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

Solution:

(a) 18 and 35

Factors of 18 are : 1, 2, 3, 6, 9 and 18

Factors of 35 are : 1, 5, 7 and 35

Since, their common factor is 1 so

18 and 35 have no common factor except 1.

Thus, 18 and 35 are co-prime numbers.

(b) 15 and 37

Factors of 15 are : 1, 3, 5 and 15

Factors of 37 are : 1, 37

Their common factor is 1, i.e. 15 and 37 do

not have common factors except 1.

Thus, 15 and 37 are co-prime numbers.

(c) 30 and 415

Factors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30

Factors of 415 are: 1, 5, 83 and 415

Their common factors are: 1 and 5

Thus, 30 and 415 are not co-prime numbers.

(d) 17 and 68

Factors of 17 are: 1 and 17

Factors of 68 are: 1, 2, 4, 17, 34 and 68

Common factors of 17 and 68 are: 1 and 17

Thus, 17 and 68 are not co-prime numbers.

(e) 216 and 215

Factors of 216 are: 1, 2, 3, 4, 6, 8, 9, 12, 18,

24, 27, 36, 54, 72, 108 and 216

Factors of 215 are: 1, 5, 43 and 215

Common factor of 216 and 215 is 1.

Thus, 216 and 215 are co-prime numbers.

(f) 81 and 16

Factors of 81 are: 1, 3, 9, 27 and 81

Factors of 16 are: 1, 2, 4, 8 and 16

Common factors of 81 and 16 is 1.

Thus, 81 and 16 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?

Solution:

The given number will be divisible by the product of 5 and 12.

The number will be divisible by 5 x 12 or 60.

Question 7.

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

Solution:

The number divisible by 12 will also be divisible by the factors of 12.

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

The number will be divisible by 1, 2, 3, 4 and 6.