Find the GCF 48 , 72

$48$ , $72$

Step 1

Find the common factors for the numerical part:

$48, 72$

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 $72$ are $1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$ .

The factors for $72$ are all numbers between $1$ and $72$ , which divide $72$ evenly.

Check numbers between $1$ and $72$

Find the factor pairs of $72$ where $x \cdot y = 72$ .

$\begin{array}{c} x & y \\ 1 & 72 \\ 2 & 36 \\ 3 & 24 \\ 4 & 18 \\ 6 & 12 \\ 8 & 9 \end{array}$

List the factors for $72$ .

$1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$

Step 4

List all the factors for $48, 72$ to find the common factors.

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

$72$ : $1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$

Step 5

The common factors for $48, 72$ are $1, 2, 3, 4, 6, 8, 12, 24$ .

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

Step 6

The GCF (HCF) of the numerical factors $1, 2, 3, 4, 6, 8, 12, 24$ is $24$ .

$24$