Pre-Algebra Examples

$18$ , $42$

Step 1

Find the common factors for the numerical part:

$18, 42$

Step 2

The factors for $18$ are $1, 2, 3, 6, 9, 18$ .

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Step 2.1

The factors for $18$ are all numbers between $1$ and $18$ , which divide $18$ evenly.

Check numbers between $1$ and $18$

Step 2.2

Find the factor pairs of $18$ where $x \cdot y = 18$ .

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

Step 2.3

List the factors for $18$ .

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

Step 3

The factors for $42$ are $1, 2, 3, 6, 7, 14, 21, 42$ .

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Step 3.1

The factors for $42$ are all numbers between $1$ and $42$ , which divide $42$ evenly.

Check numbers between $1$ and $42$

Step 3.2

Find the factor pairs of $42$ where $x \cdot y = 42$ .

$\begin{array}{c} x & y \\ 1 & 42 \\ 2 & 21 \\ 3 & 14 \\ 6 & 7 \end{array}$

Step 3.3

List the factors for $42$ .

$1, 2, 3, 6, 7, 14, 21, 42$

Step 4

List all the factors for $18, 42$ to find the common factors.

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

$42$ : $1, 2, 3, 6, 7, 14, 21, 42$

Step 5

The common factors for $18, 42$ are $1, 2, 3, 6$ .

$1, 2, 3, 6$

Step 6

The GCF (HCF) of the numerical factors $1, 2, 3, 6$ is $6$ .

$6$