Find the GCF 32 , 56

$32$ , $56$

Step 1

Find the common factors for the numerical part:

$32, 56$

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 $56$ are $1, 2, 4, 7, 8, 14, 28, 56$ .

The factors for $56$ are all numbers between $1$ and $56$ , which divide $56$ evenly.

Check numbers between $1$ and $56$

Find the factor pairs of $56$ where $x \cdot y = 56$ .

$\begin{array}{c} x & y \\ 1 & 56 \\ 2 & 28 \\ 4 & 14 \\ 7 & 8 \end{array}$

List the factors for $56$ .

$1, 2, 4, 7, 8, 14, 28, 56$

Step 4

List all the factors for $32, 56$ to find the common factors.

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

$56$ : $1, 2, 4, 7, 8, 14, 28, 56$

Step 5

The common factors for $32, 56$ are $1, 2, 4, 8$ .

$1, 2, 4, 8$

Step 6

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

$8$