What is the highest common factor of 84 and 126?

Explanation

1. 01

   Factorise both: $84 = 2^2 \times 3 \times 7$ and $126 = 2 \times 3^2 \times 7$.

2. 02

   The HCF takes the lowest power of each prime that appears in both: $2^1$, $3^1$ and $7^1$.

3. 03

   So the HCF is $2 \times 3 \times 7 = 42$.

4. 04

   Check: $84 \div 42 = 2$ and $126 \div 42 = 3$, and 2 and 3 share no factor, which confirms nothing larger will divide both.