Find the GCF 21 , 49

$21$ , $49$

Step 1

Find the common factors for the numerical part:

$21, 49$

Step 2

The factors for $21$ are $1, 3, 7, 21$ .

The factors for $21$ are all numbers between $1$ and $21$ , which divide $21$ evenly.

Check numbers between $1$ and $21$

Find the factor pairs of $21$ where $x \cdot y = 21$ .

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

List the factors for $21$ .

$1, 3, 7, 21$

Step 3

The factors for $49$ are $1, 7, 49$ .

The factors for $49$ are all numbers between $1$ and $49$ , which divide $49$ evenly.

Check numbers between $1$ and $49$

Find the factor pairs of $49$ where $x \cdot y = 49$ .

$\begin{array}{c} x & y \\ 1 & 49 \\ 7 & 7 \end{array}$

List the factors for $49$ .

$1, 7, 49$

Step 4

List all the factors for $21, 49$ to find the common factors.

$21$ : $1, 3, 7, 21$

$49$ : $1, 7, 49$

Step 5

The common factors for $21, 49$ are $1, 7$ .

$1, 7$

Step 6

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

$7$