Find the GCF 135 , 225

$135$ , $225$

Step 1

Find the common factors for the numerical part:

$135, 225$

Step 2

The factors for $135$ are $1, 3, 5, 9, 15, 27, 45, 135$ .

The factors for $135$ are all numbers between $1$ and $135$ , which divide $135$ evenly.

Check numbers between $1$ and $135$

Find the factor pairs of $135$ where $x \cdot y = 135$ .

$\begin{array}{c} x & y \\ 1 & 135 \\ 3 & 45 \\ 5 & 27 \\ 9 & 15 \end{array}$

List the factors for $135$ .

$1, 3, 5, 9, 15, 27, 45, 135$

Step 3

The factors for $225$ are $1, 3, 5, 9, 15, 25, 45, 75, 225$ .

The factors for $225$ are all numbers between $1$ and $225$ , which divide $225$ evenly.

Check numbers between $1$ and $225$

Find the factor pairs of $225$ where $x \cdot y = 225$ .

$\begin{array}{c} x & y \\ 1 & 225 \\ 3 & 75 \\ 5 & 45 \\ 9 & 25 \\ 15 & 15 \end{array}$

List the factors for $225$ .

$1, 3, 5, 9, 15, 25, 45, 75, 225$

Step 4

List all the factors for $135, 225$ to find the common factors.

$135$ : $1, 3, 5, 9, 15, 27, 45, 135$

$225$ : $1, 3, 5, 9, 15, 25, 45, 75, 225$

Step 5

The common factors for $135, 225$ are $1, 3, 5, 9, 15, 45$ .

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

Step 6

The GCF (HCF) of the numerical factors $1, 3, 5, 9, 15, 45$ is $45$ .

$45$