NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Fill in the Blanks

Question 142

Idea: Two numbers are coprime if the only factor they both share is 1.

How to understand:

1. Write the factors of each number.
2. Find the common factors.
3. If the only common factor is 1, they are coprime.

Symbol way (small steps):

We say their HCF (or GCD) is 1.

\( \text{HCF}(a,b) = 1 \)

\( \Rightarrow a \text{ and } b \text{ are coprime} \)

Example: 8 and 15

Factors of 8: 1, 2, 4, 8

Factors of 15: 1, 3, 5, 15

Common factors: 1

So, \( \text{HCF}(8,15) = 1 \)

Therefore, 8 and 15 are coprime.

Important note: Coprime does not mean “both are prime”.

Example: 14 and 25 are coprime.

\( \text{HCF}(14,25) = 1 \)

But 14 and 25 are not prime numbers.