Find the GCF 27 , 63

$27$ , $63$

Step 1

Find the common factors for the numerical part:

$27, 63$

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 $63$ are $1, 3, 7, 9, 21, 63$ .

The factors for $63$ are all numbers between $1$ and $63$ , which divide $63$ evenly.

Check numbers between $1$ and $63$

Find the factor pairs of $63$ where $x \cdot y = 63$ .

$\begin{array}{c} x & y \\ 1 & 63 \\ 3 & 21 \\ 7 & 9 \end{array}$

List the factors for $63$ .

$1, 3, 7, 9, 21, 63$

Step 4

List all the factors for $27, 63$ to find the common factors.

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

$63$ : $1, 3, 7, 9, 21, 63$

Step 5

The common factors for $27, 63$ are $1, 3, 9$ .

$1, 3, 9$

Step 6

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

$9$