Pre-Algebra Examples

$45$ , $60$

Step 1

Find the common factors for the numerical part:

$45, 60$

Step 2

The factors for $45$ are $1, 3, 5, 9, 15, 45$ .

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Step 2.1

The factors for $45$ are all numbers between $1$ and $45$ , which divide $45$ evenly.

Check numbers between $1$ and $45$

Step 2.2

Find the factor pairs of $45$ where $x \cdot y = 45$ .

$\begin{array}{c} x & y \\ 1 & 45 \\ 3 & 15 \\ 5 & 9 \end{array}$

Step 2.3

List the factors for $45$ .

$1, 3, 5, 9, 15, 45$

Step 3

The factors for $60$ are $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$ .

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Step 3.1

The factors for $60$ are all numbers between $1$ and $60$ , which divide $60$ evenly.

Check numbers between $1$ and $60$

Step 3.2

Find the factor pairs of $60$ where $x \cdot y = 60$ .

$\begin{array}{c} x & y \\ 1 & 60 \\ 2 & 30 \\ 3 & 20 \\ 4 & 15 \\ 5 & 12 \\ 6 & 10 \end{array}$

Step 3.3

List the factors for $60$ .

$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

Step 4

List all the factors for $45, 60$ to find the common factors.

$45$ : $1, 3, 5, 9, 15, 45$

$60$ : $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

Step 5

The common factors for $45, 60$ are $1, 3, 5, 15$ .

$1, 3, 5, 15$

Step 6

The GCF (HCF) of the numerical factors $1, 3, 5, 15$ is $15$ .

$15$