# What are all the factor pairs of 32?

May 22, 2016

1, 32
2, 16
4, 8

#### Explanation:

Assumption: Looking for whole number factors.

If you include fractional or decimal factors then there are infinitely many factors.

One way is to use a factor tree and then use that to build up different combinations.

From this we observe that we have the following:

$\left[1\right] \times \left[32\right] \to 1 , 32$

$\left[2\right] \times \left[2 \times 2 \times 2 \times 2\right] \to 2 , 16$

$\left[2 \times 2\right] \times \left[2 \times 2 \times 2\right] \to 4 , 8$

$\left[2 \times 2 \times 2\right] \times \left[2 \times 2\right] \to 8 , 4 \text{ "larr "repeated pair}$

$\left[2 \times 2 \times 2 \times 2\right] \times \left[2\right] \to 16 , 2 \text{ "larr "repeated pair}$

$\left[32\right] \times \left[1\right] \to 32 , 1 \text{ "larr "repeated pair}$