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).