Factors, multiples and primes Worked Solutions — GCSE Maths

Find pairs that multiply to $12$

Factors come in pairs. Look for every pair of whole numbers whose product is $12$.

Each pair gives two factors

Write out both numbers from each pair.

List them in order

Put the factors in increasing order.

Multiples are $4$ times $1$, $2$, $3$, ...

A multiple of $4$ is $4$ multiplied by a whole number.

Work them out

$4$, then keep adding $4$ each time.

State the first five

These are the first five multiples of $4$.

Recall what prime means

A prime number has exactly two factors: $1$ and the number itself.

Find the factors of $7$

The only way to make $7$ is $1\times7$, so its factors are $1$ and $7$.

Decide

It has exactly two factors, so $7$ is prime.

Find factor pairs of $20$

List pairs of numbers that multiply to $20$.

Take out $1$ and $20$

The question rules out $1$ and $20$, leaving these.

Pick one

Any of $2$, $4$, $5$ or $10$ is a correct answer.

Find factor pairs

Look for pairs of whole numbers multiplying to $18$.

Collect the factors

Take both numbers from each pair.

List in order

Arrange the factors from smallest to largest.