Examples

15

$15$ ,

50

$50$

Step 1

Find the common factors for the numerical part:

15, 50

$15, 50$

Step 2

The factors for

15

$15$ are

1, 3, 5, 15

$1, 3, 5, 15$ .

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Step 2.1

The factors for

15

$15$ are all numbers between

1

$1$ and

15

$15$ , which divide

15

$15$ evenly.

Check numbers between

1

$1$ and

15

$15$

Step 2.2

Find the factor pairs of

15

$15$ where

x \cdot y = 15

$x \cdot y = 15$ .

\begin{matrix} x & y 1 & 15 3 & 5 \end{matrix}

$\begin{array}{c} x & y \\ 1 & 15 \\ 3 & 5 \end{array}$

Step 2.3

List the factors for

15

$15$ .

1, 3, 5, 15

$1, 3, 5, 15$

1, 3, 5, 15

$1, 3, 5, 15$

Step 3

The factors for

50

$50$ are

1, 2, 5, 10, 25, 50

$1, 2, 5, 10, 25, 50$ .

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Step 3.1

The factors for

50

$50$ are all numbers between

1

$1$ and

50

$50$ , which divide

50

$50$ evenly.

Check numbers between

1

$1$ and

50

$50$

Step 3.2

Find the factor pairs of

50

$50$ where

x \cdot y = 50

$x \cdot y = 50$ .

\begin{matrix} x & y 1 & 50 2 & 25 5 & 10 \end{matrix}

$\begin{array}{c} x & y \\ 1 & 50 \\ 2 & 25 \\ 5 & 10 \end{array}$

Step 3.3

List the factors for

50

$50$ .

1, 2, 5, 10, 25, 50

$1, 2, 5, 10, 25, 50$

1, 2, 5, 10, 25, 50

$1, 2, 5, 10, 25, 50$

Step 4

List all the factors for

15, 50

$15, 50$ to find the common factors.

15

$15$ :

1, 3, 5, 15

$1, 3, 5, 15$

50

$50$ :

1, 2, 5, 10, 25, 50

$1, 2, 5, 10, 25, 50$

Step 5

The common factors for

15, 50

$15, 50$ are

1, 5

$1, 5$ .

1, 5

$1, 5$

Step 6

The GCF (HCF) of the numerical factors

1, 5

$1, 5$ is

5

$5$ .

5

$5$

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