Pre-Algebra Examples

$12$ , $6$ , $15$

Step 1

Find the common factors for the numerical part:

$12, 6, 15$

Step 2

The factors for $12$ are $1, 2, 3, 4, 6, 12$ .

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Step 2.1

The factors for $12$ are all numbers between $1$ and $12$ , which divide $12$ evenly.

Check numbers between $1$ and $12$

Step 2.2

Find the factor pairs of $12$ where $x \cdot y = 12$ .

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

Step 2.3

List the factors for $12$ .

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

Step 3

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

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Step 3.1

The factors for $6$ are all numbers between $1$ and $6$ , which divide $6$ evenly.

Check numbers between $1$ and $6$

Step 3.2

Find the factor pairs of $6$ where $x \cdot y = 6$ .

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

Step 3.3

List the factors for $6$ .

$1, 2, 3, 6$

Step 4

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

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Step 4.1

The factors for $15$ are all numbers between $1$ and $15$ , which divide $15$ evenly.

Check numbers between $1$ and $15$

Step 4.2

Find the factor pairs of $15$ where $x \cdot y = 15$ .

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

Step 4.3

List the factors for $15$ .

$1, 3, 5, 15$

Step 5

List all the factors for $12, 6, 15$ to find the common factors.

$12$ : $1, 2, 3, 4, 6, 12$

$6$ : $1, 2, 3, 6$

$15$ : $1, 3, 5, 15$

Step 6

The common factors for $12, 6, 15$ are $1, 3$ .

$1, 3$

Step 7

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

$3$