Find the GCF 27 , 125

$27$ , $125$

Step 1

Find the common factors for the numerical part:

$27, 125$

Step 2

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

The factors for $27$ are all numbers between $1$ and $27$ , which divide $27$ evenly.

Check numbers between $1$ and $27$

Find the factor pairs of $27$ where $x \cdot y = 27$ .

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

List the factors for $27$ .

$1, 3, 9, 27$

Step 3

The factors for $125$ are $1, 5, 25, 125$ .

The factors for $125$ are all numbers between $1$ and $125$ , which divide $125$ evenly.

Check numbers between $1$ and $125$

Find the factor pairs of $125$ where $x \cdot y = 125$ .

$\begin{array}{c} x & y \\ 1 & 125 \\ 5 & 25 \end{array}$

List the factors for $125$ .

$1, 5, 25, 125$

Step 4

List all the factors for $27, 125$ to find the common factors.

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

$125$ : $1, 5, 25, 125$

Step 5

The common factors for $27, 125$ are $1$ .

$1$

Step 6

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

$1$