Algebra Examples

$30$ , $48$

Step 1

Find the common factors for the numerical part:

$30, 48$

Step 2

The factors for $30$ are $1, 2, 3, 5, 6, 10, 15, 30$ .

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Step 2.1

The factors for $30$ are all numbers between $1$ and $30$ , which divide $30$ evenly.

Check numbers between $1$ and $30$

Step 2.2

Find the factor pairs of $30$ where $x \cdot y = 30$ .

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

Step 2.3

List the factors for $30$ .

$1, 2, 3, 5, 6, 10, 15, 30$

Step 3

The factors for $48$ are $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$ .

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Step 3.1

The factors for $48$ are all numbers between $1$ and $48$ , which divide $48$ evenly.

Check numbers between $1$ and $48$

Step 3.2

Find the factor pairs of $48$ where $x \cdot y = 48$ .

$\begin{array}{c} x & y \\ 1 & 48 \\ 2 & 24 \\ 3 & 16 \\ 4 & 12 \\ 6 & 8 \end{array}$

Step 3.3

List the factors for $48$ .

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

Step 4

List all the factors for $30, 48$ to find the common factors.

$30$ : $1, 2, 3, 5, 6, 10, 15, 30$

$48$ : $1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

Step 5

The common factors for $30, 48$ are $1, 2, 3, 6$ .

$1, 2, 3, 6$

Step 6

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

$6$