Find the GCF 30 , 18 , 36

$30$ , $18$ , $36$

Step 1

Find the common factors for the numerical part:

$30, 18, 36$

Step 2

The factors for $30$ are $1, 2, 3, 5, 6, 10, 15, 30$ .

The factors for $30$ are all numbers between $1$ and $30$ , which divide $30$ evenly.

Check numbers between $1$ and $30$

Find the factor pairs of $30$ where $x \cdot y = 30$ .

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

List the factors for $30$ .

$1, 2, 3, 5, 6, 10, 15, 30$

Step 3

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

The factors for $18$ are all numbers between $1$ and $18$ , which divide $18$ evenly.

Check numbers between $1$ and $18$

Find the factor pairs of $18$ where $x \cdot y = 18$ .

$\begin{array}{c} x & y \\ 1 & 18 \\ 2 & 9 \\ 3 & 6 \end{array}$

List the factors for $18$ .

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

Step 4

The factors for $36$ are $1, 2, 3, 4, 6, 9, 12, 18, 36$ .

The factors for $36$ are all numbers between $1$ and $36$ , which divide $36$ evenly.

Check numbers between $1$ and $36$

Find the factor pairs of $36$ where $x \cdot y = 36$ .

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

List the factors for $36$ .

$1, 2, 3, 4, 6, 9, 12, 18, 36$

Step 5

List all the factors for $30, 18, 36$ to find the common factors.

$30$ : $1, 2, 3, 5, 6, 10, 15, 30$

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

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

Step 6

The common factors for $30, 18, 36$ are $1, 2, 3, 6$ .

$1, 2, 3, 6$

Step 7

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

$6$