Find the GCF 45 , 18

$45$ , $18$

Step 1

Find the common factors for the numerical part:

$45, 18$

Step 2

The factors for $45$ are $1, 3, 5, 9, 15, 45$ .

The factors for $45$ are all numbers between $1$ and $45$ , which divide $45$ evenly.

Check numbers between $1$ and $45$

Find the factor pairs of $45$ where $x \cdot y = 45$ .

$\begin{array}{c} x & y \\ 1 & 45 \\ 3 & 15 \\ 5 & 9 \end{array}$

List the factors for $45$ .

$1, 3, 5, 9, 15, 45$

Step 3

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 4

List all the factors for $45, 18$ to find the common factors.

$45$ : $1, 3, 5, 9, 15, 45$

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

Step 5

The common factors for $45, 18$ are $1, 3, 9$ .

$1, 3, 9$

Step 6

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

$9$