Find the GCF 72 , 84

$72$ , $84$

Step 1

Find the common factors for the numerical part:

$72, 84$

Step 2

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 3

The factors for $84$ are $1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$ .

The factors for $84$ are all numbers between $1$ and $84$ , which divide $84$ evenly.

Check numbers between $1$ and $84$

Find the factor pairs of $84$ where $x \cdot y = 84$ .

$\begin{array}{c} x & y \\ 1 & 84 \\ 2 & 42 \\ 3 & 28 \\ 4 & 21 \\ 6 & 14 \\ 7 & 12 \end{array}$

List the factors for $84$ .

$1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$

Step 4

List all the factors for $72, 84$ to find the common factors.

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

$84$ : $1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$

Step 5

The common factors for $72, 84$ are $1, 2, 3, 4, 6, 12$ .

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

Step 6

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

$12$