Find the GCF 25 , 75

$25$ , $75$

Step 1

Find the common factors for the numerical part:

$25, 75$

Step 2

The factors for $25$ are $1, 5, 25$ .

The factors for $25$ are all numbers between $1$ and $25$ , which divide $25$ evenly.

Check numbers between $1$ and $25$

Find the factor pairs of $25$ where $x \cdot y = 25$ .

$\begin{array}{c} x & y \\ 1 & 25 \\ 5 & 5 \end{array}$

List the factors for $25$ .

$1, 5, 25$

Step 3

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

The factors for $75$ are all numbers between $1$ and $75$ , which divide $75$ evenly.

Check numbers between $1$ and $75$

Find the factor pairs of $75$ where $x \cdot y = 75$ .

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

List the factors for $75$ .

$1, 3, 5, 15, 25, 75$

Step 4

List all the factors for $25, 75$ to find the common factors.

$25$ : $1, 5, 25$

$75$ : $1, 3, 5, 15, 25, 75$

Step 5

The common factors for $25, 75$ are $1, 5, 25$ .

$1, 5, 25$

Step 6

The GCF (HCF) of the numerical factors $1, 5, 25$ is $25$ .

$25$