Prime factorisation Worked Solutions — GCSE Maths

Split 12 into a factor pair

Start a factor tree by breaking 12 into any two factors.

Break down until all prime

$4$ splits into $2 \times 2$, and $3$ is already prime.

Write in index form

Two $2$s become $2²$, giving $12 = 2² \times 3$.

Split 18

Break 18 into 2 and 9.

Break down 9

$9$ splits into $3 \times 3$, and $2$ is prime.

Write in index form

Two $3$s become $3²$, giving $18 = 2 \times 3²$.

Split 20

Break 20 into 4 and 5.

Break down 4

$4$ splits into $2 \times 2$, and $5$ is prime.

Write in index form

So $20 = 2² \times 5$.

Split 24

Break 24 into 8 and 3.

Break down 8

8 splits into three 2s, and 3 is prime.

Write in index form

So $24 = 2³ \times 3$.

Split 30

Break 30 into 6 and 5.

Break down 6

$6$ splits into $2 \times 3$, and $5$ is prime.

Write as a product of primes

So $30 = 2 \times 3 \times 5$ (no index needed, each appears once).