Find the GCF 28 , 63

$28$ , $63$

Step 1

Find the common factors for the numerical part:

$28, 63$

Step 2

The factors for $28$ are $1, 2, 4, 7, 14, 28$ .

The factors for $28$ are all numbers between $1$ and $28$ , which divide $28$ evenly.

Check numbers between $1$ and $28$

Find the factor pairs of $28$ where $x \cdot y = 28$ .

$\begin{array}{c} x & y \\ 1 & 28 \\ 2 & 14 \\ 4 & 7 \end{array}$

List the factors for $28$ .

$1, 2, 4, 7, 14, 28$

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 $28, 63$ to find the common factors.

$28$ : $1, 2, 4, 7, 14, 28$

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

Step 5

The common factors for $28, 63$ are $1, 7$ .

$1, 7$

Step 6

The GCF (HCF) of the numerical factors $1, 7$ is $7$ .

$7$