Which pair of numbers below is NOT co-prime?

Class 6Playing with NumbersPlaying with Numbers

A14 and 15
B18 and 25
C21 and 35
D8 and 27

Step-by-Step Solution

21 =

3 \times 7

and

35 = 5 \times 7

both contain 7, so their HCF is 7, not 1. The other pairs share no prime:

14 = 2 \times 7

with

15 = 3 \times 5, 18 = 2 \times 3 \times 3

with

25 = 5 \times 5

, and

8 = 2 \times 2 \times 2

with

27 = 3 \times 3 \times 3

— all have HCF 1. The trap is thinking two odd numbers, or two composites, cannot share a factor.

Answer: C) 21 and 35

Key idea: Prime vs composite

A whole number greater than 1 is **prime** if it has exactly two factors: 1 and itself. It is **composite** if it has more than two factors. The number 1 is neither prime nor composite (it has only one factor — itself). 2 is the only **even** prime; every other even number is divisible by 2 and so has at least three factors.

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