Find the GCF 30 , 12

$30$ , $12$

Step 1

Find the common factors for the numerical part:

$30, 12$

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

The factors for $12$ are all numbers between $1$ and $12$ , which divide $12$ evenly.

Check numbers between $1$ and $12$

Find the factor pairs of $12$ where $x \cdot y = 12$ .

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

List the factors for $12$ .

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

Step 4

List all the factors for $30, 12$ to find the common factors.

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

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

Step 5

The common factors for $30, 12$ are $1, 2, 3, 6$ .

$1, 2, 3, 6$

Step 6

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

$6$