Find the GCF 18 , 81 , 144

$18$ , $81$ , $144$

Step 1

Find the common factors for the numerical part:

$18, 81, 144$

Step 2

The factors for $18$ are $1, 2, 3, 6, 9, 18$ .

The factors for $18$ are all numbers between $1$ and $18$ , which divide $18$ evenly.

Check numbers between $1$ and $18$

Find the factor pairs of $18$ where $x \cdot y = 18$ .

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

List the factors for $18$ .

$1, 2, 3, 6, 9, 18$

Step 3

The factors for $81$ are $1, 3, 9, 27, 81$ .

The factors for $81$ are all numbers between $1$ and $81$ , which divide $81$ evenly.

Check numbers between $1$ and $81$

Find the factor pairs of $81$ where $x \cdot y = 81$ .

$\begin{array}{c} x & y \\ 1 & 81 \\ 3 & 27 \\ 9 & 9 \end{array}$

List the factors for $81$ .

$1, 3, 9, 27, 81$

Step 4

The factors for $144$ are $1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144$ .

The factors for $144$ are all numbers between $1$ and $144$ , which divide $144$ evenly.

Check numbers between $1$ and $144$

Find the factor pairs of $144$ where $x \cdot y = 144$ .

$\begin{array}{c} x & y \\ 1 & 144 \\ 2 & 72 \\ 3 & 48 \\ 4 & 36 \\ 6 & 24 \\ 8 & 18 \\ 9 & 16 \\ 12 & 12 \end{array}$

List the factors for $144$ .

$1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144$

Step 5

List all the factors for $18, 81, 144$ to find the common factors.

$18$ : $1, 2, 3, 6, 9, 18$

$81$ : $1, 3, 9, 27, 81$

$144$ : $1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144$

Step 6

The common factors for $18, 81, 144$ are $1, 3, 9$ .

$1, 3, 9$

Step 7

The GCF (HCF) of the numerical factors $1, 3, 9$ is $9$ .

$9$