Find the GCF 24 , 36 , 108

$24$ , $36$ , $108$

Step 1

Find the common factors for the numerical part:

$24, 36, 108$

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 $36$ are $1, 2, 3, 4, 6, 9, 12, 18, 36$ .

The factors for $36$ are all numbers between $1$ and $36$ , which divide $36$ evenly.

Check numbers between $1$ and $36$

Find the factor pairs of $36$ where $x \cdot y = 36$ .

$\begin{array}{c} x & y \\ 1 & 36 \\ 2 & 18 \\ 3 & 12 \\ 4 & 9 \\ 6 & 6 \end{array}$

List the factors for $36$ .

$1, 2, 3, 4, 6, 9, 12, 18, 36$

Step 4

The factors for $108$ are $1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108$ .

The factors for $108$ are all numbers between $1$ and $108$ , which divide $108$ evenly.

Check numbers between $1$ and $108$

Find the factor pairs of $108$ where $x \cdot y = 108$ .

$\begin{array}{c} x & y \\ 1 & 108 \\ 2 & 54 \\ 3 & 36 \\ 4 & 27 \\ 6 & 18 \\ 9 & 12 \end{array}$

List the factors for $108$ .

$1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108$

Step 5

List all the factors for $24, 36, 108$ to find the common factors.

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

$36$ : $1, 2, 3, 4, 6, 9, 12, 18, 36$

$108$ : $1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108$

Step 6

The common factors for $24, 36, 108$ are $1, 2, 3, 4, 6, 12$ .

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

Step 7

The GCF (HCF) of the numerical factors $1, 2, 3, 4, 6, 12$ is $12$ .

$12$