Find the GCF 32 , 72

$32$ , $72$

Step 1

Find the common factors for the numerical part:

$32, 72$

Step 2

The factors for $32$ are $1, 2, 4, 8, 16, 32$ .

The factors for $32$ are all numbers between $1$ and $32$ , which divide $32$ evenly.

Check numbers between $1$ and $32$

Find the factor pairs of $32$ where $x \cdot y = 32$ .

$\begin{array}{c} x & y \\ 1 & 32 \\ 2 & 16 \\ 4 & 8 \end{array}$

List the factors for $32$ .

$1, 2, 4, 8, 16, 32$

Step 3

The factors for $72$ are $1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$ .

The factors for $72$ are all numbers between $1$ and $72$ , which divide $72$ evenly.

Check numbers between $1$ and $72$

Find the factor pairs of $72$ where $x \cdot y = 72$ .

$\begin{array}{c} x & y \\ 1 & 72 \\ 2 & 36 \\ 3 & 24 \\ 4 & 18 \\ 6 & 12 \\ 8 & 9 \end{array}$

List the factors for $72$ .

$1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$

Step 4

List all the factors for $32, 72$ to find the common factors.

$32$ : $1, 2, 4, 8, 16, 32$

$72$ : $1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$

Step 5

The common factors for $32, 72$ are $1, 2, 4, 8$ .

$1, 2, 4, 8$

Step 6

The GCF (HCF) of the numerical factors $1, 2, 4, 8$ is $8$ .

$8$