Using prime factorisation, find the highest common factor (HCF) of 72 and 108.

Explanation

1. 01

   $72 = 2^3 \times 3^2$ and $108 = 2^2 \times 3^3$.

2. 02

   HCF takes the LOWEST power of each common prime: $2^2 \times 3^2$.

3. 03

   $\operatorname{HCF} = 4 \times 9 = 36$.