Examples

$6$ ,

$9$ ,

$12$

Step 1

Find the common factors for the numerical part:

$6, 9, 12$

Step 2

The factors for

$6$ are

$1, 2, 3, 6$ .

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Step 2.1

The factors for

$6$ are all numbers between

$1$ and

$6$ , which divide

$6$ evenly.

Check numbers between

$1$ and

$6$

Step 2.2

Find the factor pairs of

$6$ where

$x \cdot y = 6$ .

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

Step 2.3

List the factors for

$6$ .

$1, 2, 3, 6$

Step 3

The factors for

$9$ are

$1, 3, 9$ .

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Step 3.1

The factors for

$9$ are all numbers between

$1$ and

$9$ , which divide

$9$ evenly.

Check numbers between

$1$ and

$9$

Step 3.2

Find the factor pairs of

$9$ where

$x \cdot y = 9$ .

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

Step 3.3

List the factors for

$9$ .

$1, 3, 9$

Step 4

The factors for

$12$ are

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

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Step 4.1

The factors for

$12$ are all numbers between

$1$ and

$12$ , which divide

$12$ evenly.

Check numbers between

$1$ and

$12$

Step 4.2

Find the factor pairs of

$12$ where

$x \cdot y = 12$ .

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

Step 4.3

List the factors for

$12$ .

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

Step 5

List all the factors for

$6, 9, 12$ to find the common factors.

$6$ :

$1, 2, 3, 6$

$9$ :

$1, 3, 9$

$12$ :

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

Step 6

The common factors for

$6, 9, 12$ are

$1, 3$ .

$1, 3$

Step 7

The GCF (HCF) of the numerical factors

$1, 3$ is

$3$ .

$3$

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