Precalculus Examples

$13$ and $26$

Step 1

Find the common factors for the numerical part:

$13, 26$

Step 2

The factors for $13$ are $1, 13$ .

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Step 2.1

The factors for $13$ are all numbers between $1$ and $13$ , which divide $13$ evenly.

Check numbers between $1$ and $13$

Step 2.2

Find the factor pairs of $13$ where $x \cdot y = 13$ .

$\begin{array}{c} x & y \\ 1 & 13 \end{array}$

Step 2.3

List the factors for $13$ .

$1, 13$

Step 3

The factors for $26$ are $1, 2, 13, 26$ .

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Step 3.1

The factors for $26$ are all numbers between $1$ and $26$ , which divide $26$ evenly.

Check numbers between $1$ and $26$

Step 3.2

Find the factor pairs of $26$ where $x \cdot y = 26$ .

$\begin{array}{c} x & y \\ 1 & 26 \\ 2 & 13 \end{array}$

Step 3.3

List the factors for $26$ .

$1, 2, 13, 26$

Step 4

List all the factors for $13, 26$ to find the common factors.

$13$ : $1, 13$

$26$ : $1, 2, 13, 26$

Step 5

The common factors for $13, 26$ are $1, 13$ .

$1, 13$

Step 6

The GCF (HCF) of the numerical factors $1, 13$ is $13$ .

$13$