Find the GCF 72 90

$72$ $90$

Step 1

Find the common factors for the numerical part:

$72, 90$

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 $90$ are $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$ .

The factors for $90$ are all numbers between $1$ and $90$ , which divide $90$ evenly.

Check numbers between $1$ and $90$

Find the factor pairs of $90$ where $x \cdot y = 90$ .

$\begin{array}{c} x & y \\ 1 & 90 \\ 2 & 45 \\ 3 & 30 \\ 5 & 18 \\ 6 & 15 \\ 9 & 10 \end{array}$

List the factors for $90$ .

$1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

Step 4

List all the factors for $72, 90$ to find the common factors.

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

$90$ : $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

Step 5

The common factors for $72, 90$ are $1, 2, 3, 6, 9, 18$ .

$1, 2, 3, 6, 9, 18$

Step 6

The GCF (HCF) of the numerical factors $1, 2, 3, 6, 9, 18$ is $18$ .

$18$