Find the GCF 8 , 24 , 64

$8$ , $24$ , $64$

Step 1

Find the common factors for the numerical part:

$8, 24, 64$

Step 2

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

The factors for $8$ are all numbers between $1$ and $8$ , which divide $8$ evenly.

Check numbers between $1$ and $8$

Find the factor pairs of $8$ where $x \cdot y = 8$ .

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

List the factors for $8$ .

$1, 2, 4, 8$

Step 3

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 4

The factors for $64$ are $1, 2, 4, 8, 16, 32, 64$ .

The factors for $64$ are all numbers between $1$ and $64$ , which divide $64$ evenly.

Check numbers between $1$ and $64$

Find the factor pairs of $64$ where $x \cdot y = 64$ .

$\begin{array}{c} x & y \\ 1 & 64 \\ 2 & 32 \\ 4 & 16 \\ 8 & 8 \end{array}$

List the factors for $64$ .

$1, 2, 4, 8, 16, 32, 64$

Step 5

List all the factors for $8, 24, 64$ to find the common factors.

$8$ : $1, 2, 4, 8$

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

$64$ : $1, 2, 4, 8, 16, 32, 64$

Step 6

The common factors for $8, 24, 64$ are $1, 2, 4, 8$ .

$1, 2, 4, 8$

Step 7

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

$8$