Co-prime Numbers

Class 6 Maths · Chapter 5: Prime Time · NCERT Ganita Prakash section 5.3

Learn

Two numbers are co-prime when their only common factor is 1. 8 and 15 are co-prime: factors of 8 are 1, 2, 4, 8 and factors of 15 are 1, 3, 5, 15. Only 1 is shared.

common factor: only 1

Co-prime numbers do not have to be prime! 8 and 15 are both composite, but they are still co-prime. And 12 and 18 are not co-prime: both divide by 2, 3 and 6.

Tenzin's two fairy lights blink together, then one blinks every 4 seconds and the other every 9 seconds. Because 4 and 9 are co-prime, they next blink together after 4 × 9 = 36 seconds.

4 × 9 = 36

Explore: sort the pairs. Which ones are co-prime?

Tap every co-prime pair.
Two lights blink every 5 and 6 seconds. Find on the line when they next blink together.

Remember

Co-prime: the only common factor is 1. They need not be prime (8 and 15).
For co-prime numbers, the first common multiple is their product.

Quick check

Which pair is co-prime?

6 and 9
10 and 15
9 and 16
12 and 20

Answer

9 and 16. 9 = 3 × 3 and 16 = 2 × 2 × 2 × 2 share no factor except 1.

Think about it

Are two numbers next to each other, like 20 and 21, always co-prime? Why?

One answer

Yes. If a number bigger than 1 divided both, it would also divide their difference, which is 1. Nothing bigger than 1 divides 1.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.