Find the GCF 24 , 40 , 56

$24$ , $40$ , $56$

Step 1

Find the common factors for the numerical part:

$24, 40, 56$

Step 2

The factors for $24$ are $1, 2, 3, 4, 6, 8, 12, 24$ .

The factors for $24$ are all numbers between $1$ and $24$ , which divide $24$ evenly.

Check numbers between $1$ and $24$

Find the factor pairs of $24$ where $x \cdot y = 24$ .

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

List the factors for $24$ .

$1, 2, 3, 4, 6, 8, 12, 24$

Step 3

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 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 $24, 40, 56$ to find the common factors.

$24$ : $1, 2, 3, 4, 6, 8, 12, 24$

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

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

Step 6

The common factors for $24, 40, 56$ are $1, 2, 4, 8$ .

$1, 2, 4, 8$

Step 7

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

$8$