Students can download Chapter 3 Playing with Numbers Ex 3.4 KSEEB Solutions for Class 6 Maths helps you to revise the complete syllabus.

## Karnataka State Syllabus Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4

The factors of 50 are the natural numbers that divide the original number, evenly. They are 1,2,5,10,25 and 50.

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

There are two ways to find the factors of 18: using factor pairs, and using prime factorization.

Question 5.

Which of the following numbers is 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 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.

Here is the list of all Postive Factors of 24 in numerical order: 1, 2, 3, 4, 6, 8, 12, and 24.

Question 6.

A number is divisible by both 5 and 12. By which other numbers 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 factor of these numbers 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.