Find the HCF of 72 and 108 by prime factorisation.

Class 6Playing with NumbersPlaying with Numbers

A12
B18
C36
D216

Step-by-Step Solution

72 =

2 \times 2 \times 2 \times 3 \times 3

and

108 = 2 \times 2 \times 3 \times 3 \times 3

. Take the primes they share, each the smaller number of times:

2 \times 2 \times 3 \times 3 = 36

. The trap is 216, which is the LCM — that comes from taking each prime the LARGER number of times.

Answer: C) 36

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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