Find the GCF 12 , 20 , 56

$12$ , $20$ , $56$

Step 1

Find the common factors for the numerical part:

$12, 20, 56$

Step 2

The factors for $12$ are $1, 2, 3, 4, 6, 12$ .

The factors for $12$ are all numbers between $1$ and $12$ , which divide $12$ evenly.

Check numbers between $1$ and $12$

Find the factor pairs of $12$ where $x \cdot y = 12$ .

$\begin{array}{c} x & y \\ 1 & 12 \\ 2 & 6 \\ 3 & 4 \end{array}$

List the factors for $12$ .

$1, 2, 3, 4, 6, 12$

Step 3

The factors for $20$ are $1, 2, 4, 5, 10, 20$ .

The factors for $20$ are all numbers between $1$ and $20$ , which divide $20$ evenly.

Check numbers between $1$ and $20$

Find the factor pairs of $20$ where $x \cdot y = 20$ .

$\begin{array}{c} x & y \\ 1 & 20 \\ 2 & 10 \\ 4 & 5 \end{array}$

List the factors for $20$ .

$1, 2, 4, 5, 10, 20$

Step 4

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 5

List all the factors for $12, 20, 56$ to find the common factors.

$12$ : $1, 2, 3, 4, 6, 12$

$20$ : $1, 2, 4, 5, 10, 20$

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

Step 6

The common factors for $12, 20, 56$ are $1, 2, 4$ .

$1, 2, 4$

Step 7

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

$4$