Precalculus Examples

18

$18$ and

24

$24$

Step 1

Find the common factors for the numerical part:

18, 24

$18, 24$

Step 2

The factors for

18

$18$ are

1, 2, 3, 6, 9, 18

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

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Step 2.1

The factors for

18

$18$ are all numbers between

1

$1$ and

18

$18$ , which divide

18

$18$ evenly.

Check numbers between

1

$1$ and

18

$18$

Step 2.2

Find the factor pairs of

18

$18$ where

x \cdot y = 18

$x \cdot y = 18$ .

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

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

Step 2.3

List the factors for

18

$18$ .

1, 2, 3, 6, 9, 18

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

1, 2, 3, 6, 9, 18

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

Step 3

The factors for

24

$24$ are

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

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

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Step 3.1

The factors for

24

$24$ are all numbers between

1

$1$ and

24

$24$ , which divide

24

$24$ evenly.

Check numbers between

1

$1$ and

24

$24$

Step 3.2

Find the factor pairs of

24

$24$ where

x \cdot y = 24

$x \cdot y = 24$ .

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

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

Step 3.3

List the factors for

24

$24$ .

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

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

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

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

Step 4

List all the factors for

18, 24

$18, 24$ to find the common factors.

18

$18$ :

1, 2, 3, 6, 9, 18

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

24

$24$ :

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

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

Step 5

The common factors for

18, 24

$18, 24$ are

1, 2, 3, 6

$1, 2, 3, 6$ .

1, 2, 3, 6

$1, 2, 3, 6$

Step 6

The GCF (HCF) of the numerical factors

1, 2, 3, 6

$1, 2, 3, 6$ is

6

$6$ .

6

$6$