Examples

4

$4$ ,

12

$12$ ,

48

$48$

Step 1

Find the common factors for the numerical part:

4, 12, 48

$4, 12, 48$

Step 2

The factors for

4

$4$ are

1, 2, 4

$1, 2, 4$ .

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Step 2.1

The factors for

4

$4$ are all numbers between

1

$1$ and

4

$4$ , which divide

4

$4$ evenly.

Check numbers between

1

$1$ and

4

$4$

Step 2.2

Find the factor pairs of

4

$4$ where

x \cdot y = 4

$x \cdot y = 4$ .

\begin{matrix} x & y 1 & 4 2 & 2 \end{matrix}

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

Step 2.3

List the factors for

4

$4$ .

1, 2, 4

$1, 2, 4$

1, 2, 4

$1, 2, 4$

Step 3

The factors for

12

$12$ are

1, 2, 3, 4, 6, 12

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

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Step 3.1

The factors for

12

$12$ are all numbers between

1

$1$ and

12

$12$ , which divide

12

$12$ evenly.

Check numbers between

1

$1$ and

12

$12$

Step 3.2

Find the factor pairs of

12

$12$ where

x \cdot y = 12

$x \cdot y = 12$ .

\begin{matrix} x & y 1 & 12 2 & 6 3 & 4 \end{matrix}

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

Step 3.3

List the factors for

12

$12$ .

1, 2, 3, 4, 6, 12

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

1, 2, 3, 4, 6, 12

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

Step 4

The factors for

48

$48$ are

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$ .

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Step 4.1

The factors for

48

$48$ are all numbers between

1

$1$ and

48

$48$ , which divide

$48$ evenly.

Check numbers between

$1$ and

$48$

Step 4.2

Find the factor pairs of

$48$ where

$x \cdot y = 48$ .

$\begin{array}{c} x & y \\ 1 & 48 \\ 2 & 24 \\ 3 & 16 \\ 4 & 12 \\ 6 & 8 \end{array}$

Step 4.3

List the factors for

$48$ .

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

Step 5

List all the factors for

$4, 12, 48$ to find the common factors.

$4$ :

$1, 2, 4$

$12$ :

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

$48$ :

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

Step 6

The common factors for

$4, 12, 48$ are

$1, 2, 4$ .

$1, 2, 4$

Step 7

The GCF (HCF) of the numerical factors

$1, 2, 4$ is

$4$ .

$4$

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