Skill: Identify factor pairs

A factor pair is two whole numbers that multiply to make a given number.

For example, to find the factor pairs of $24$, look for multiplication facts with a product of $24$.

1. Start with $1$:

$$1 \times 24=24$$

So, $(1,24)$ is a factor pair.

2. Try $2$:

$$2 \times 12=24$$

So, $(2,12)$ is a factor pair.

3. Try $3$:

$$3 \times 8=24$$

So, $(3,8)$ is a factor pair.

4. Try $4$:

$$4 \times 6=24$$

So, $(4,6)$ is a factor pair.

Now the pairs have started repeating in reverse. For example, $6 \times 4$ is the same pair as $4 \times 6$, so it is not a new unordered factor pair.

Therefore, the complete set of factor pairs for $24$ is

$$(1,24),\ (2,12),\ (3,8),\ (4,6)$$

You can also picture each pair as a rectangular array. For example, $4 \times 6$ makes an array with $4$ rows and $6$ columns, for a total of $24$ objects.

Remember: factors are numbers that multiply to make a given number. Multiples are the numbers you get when you keep multiplying a number by $1,2,3,\ldots$ For example, $2,4,6,8$ are multiples of $2$, but $2$ and $12$ are factors in the factor pair $(2,12)$ for $24$.