Find the GCF 28 , 20 , 40

$28$ , $20$ , $40$

Step 1

Find the common factors for the numerical part:

$28, 20, 40$

Step 2

The factors for $28$ are $1, 2, 4, 7, 14, 28$ .

The factors for $28$ are all numbers between $1$ and $28$ , which divide $28$ evenly.

Check numbers between $1$ and $28$

Find the factor pairs of $28$ where $x \cdot y = 28$ .

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

List the factors for $28$ .

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

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 $40$ are $1, 2, 4, 5, 8, 10, 20, 40$ .

The factors for $40$ are all numbers between $1$ and $40$ , which divide $40$ evenly.

Check numbers between $1$ and $40$

Find the factor pairs of $40$ where $x \cdot y = 40$ .

$\begin{array}{c} x & y \\ 1 & 40 \\ 2 & 20 \\ 4 & 10 \\ 5 & 8 \end{array}$

List the factors for $40$ .

$1, 2, 4, 5, 8, 10, 20, 40$

Step 5

List all the factors for $28, 20, 40$ to find the common factors.

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

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

$40$ : $1, 2, 4, 5, 8, 10, 20, 40$

Step 6

The common factors for $28, 20, 40$ are $1, 2, 4$ .

$1, 2, 4$

Step 7

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

$4$