Find the GCF 48 21

$48$ $21$

Step 1

Find the common factors for the numerical part:

$48, 21$

Step 2

The factors for $48$ are $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$ .

The factors for $48$ are all numbers between $1$ and $48$ , which divide $48$ evenly.

Check numbers between $1$ and $48$

Find the factor pairs of $48$ where $x \cdot y = 48$ .

$\begin{array}{c} x & y \\ 1 & 48 \\ 2 & 24 \\ 3 & 16 \\ 4 & 12 \\ 6 & 8 \end{array}$

List the factors for $48$ .

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

Step 3

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 4

List all the factors for $48, 21$ to find the common factors.

$48$ : $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

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

Step 5

The common factors for $48, 21$ are $1, 3$ .

$1, 3$

Step 6

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

$3$