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## Karnataka State Syllabus Class 6 Maths Chapter 3 Playing with Numbers Ex 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

Solution:

Question 2.

Find the common factors of

a) 4, 8 and 12

b) 5, 15 and 25

Solution:

Question 3.

Find first three common multiples of:

a) 6 and 8

b) 12 and 18

Solution:

a) 6 and 8:-

3 common multiples = 24, 48, 72

b) 12 and 18:-

Multiples of 12 = 12, 24, 36, 48, 60, 72

Multiples of 18= 18, 36, 54, 72

3 Common multiples = 36, 72, 108

Question 4.

Write all the number less than 10(1 which are common multiples of 3 and 4

Solution:

Multiples of 3 = 3, 6, 0, 12, 15, 18, 21, 24, 27, 30

Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

Common multiples = 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

Solution:

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

Factors of 35 = 1, 5, 7, 35

Common factors = 1

Therefore, the given two numbers are co-prime

b) Factors of 15 = 1, 3, 5, 15

Factors of 37 = 1, 37

Common factors = 1

The given two numbers are co-prime

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

Factors of 415 = 1, 5, 83, 415

Common factors = 1, 5

As these numbers have a common factors other than 1, the given two numbers arc not co-prime

d) Factors of 17 = 1, 17

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

Common factors = 1, 17

As these numbers have a common factors other than 1, the given two numbers are not co-prime

e) Factors of 216 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 17, 36, 54, 72, 108, 216

Factors of 215 = 1, 5, 43, 215

Common factors = 1

The given two numbers are prime.

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

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

Common factors = 1

Therefore the given two numbers are co-prime.

Question 6.

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

Solution:

Factors of 5 = 1, 5

Factors of 12 = 1, 2, 3, 4, 5, 6, 12

As the common factors of these number is 1, the given two numbers are co-prime and the number will also be divisible by their product , i,e 60 and the factors of 60.

i.e, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Question 7.

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

Solution:

Since, the number is divisible by 12, it will also be divisible 1,2,3,4 and 6 are numbers other than 12 by which this number is also divisible.