Pre-Algebra Examples

$12$ , $28$ , $24$

Step 1

Find the common factors for the numerical part:

$12, 28, 24$

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 $28$ are $1, 2, 4, 7, 14, 28$ .

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Step 3.1

The factors for $28$ are all numbers between $1$ and $28$ , which divide $28$ evenly.

Check numbers between $1$ and $28$

Step 3.2

Find the factor pairs of $28$ where $x \cdot y = 28$ .

$\begin{array}{c} x & y \\ 1 & 28 \\ 2 & 14 \\ 4 & 7 \end{array}$

Step 3.3

List the factors for $28$ .

$1, 2, 4, 7, 14, 28$

Step 4

The factors for $24$ are $1, 2, 3, 4, 6, 8, 12, 24$ .

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Step 4.1

The factors for $24$ are all numbers between $1$ and $24$ , which divide $24$ evenly.

Check numbers between $1$ and $24$

Step 4.2

Find the factor pairs of $24$ where $x \cdot y = 24$ .

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

Step 4.3

List the factors for $24$ .

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

Step 5

List all the factors for $12, 28, 24$ to find the common factors.

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

$28$ : $1, 2, 4, 7, 14, 28$

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

Step 6

The common factors for $12, 28, 24$ are $1, 2, 4$ .

$1, 2, 4$

Step 7

The GCF (HCF) of the numerical factors $1, 2, 4$ is $4$ .

$4$