Pre-Algebra Examples

$54$ , $45$ , $33$ , $39$ , $48$ , $40$ , $21$

Step 1

Find the common factors for the numerical part:

$54, 45, 33, 39, 48, 40, 21$

Step 2

The factors for $54$ are $1, 2, 3, 6, 9, 18, 27, 54$ .

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Step 2.1

The factors for $54$ are all numbers between $1$ and $54$ , which divide $54$ evenly.

Check numbers between $1$ and $54$

Step 2.2

Find the factor pairs of $54$ where $x \cdot y = 54$ .

$\begin{array}{c} x & y \\ 1 & 54 \\ 2 & 27 \\ 3 & 18 \\ 6 & 9 \end{array}$

Step 2.3

List the factors for $54$ .

$1, 2, 3, 6, 9, 18, 27, 54$

Step 3

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

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Step 3.1

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

Check numbers between $1$ and $45$

Step 3.2

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 3.3

List the factors for $45$ .

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

Step 4

The factors for $33$ are $1, 3, 11, 33$ .

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Step 4.1

The factors for $33$ are all numbers between $1$ and $33$ , which divide $33$ evenly.

Check numbers between $1$ and $33$

Step 4.2

Find the factor pairs of $33$ where $x \cdot y = 33$ .

$\begin{array}{c} x & y \\ 1 & 33 \\ 3 & 11 \end{array}$

Step 4.3

List the factors for $33$ .

$1, 3, 11, 33$

Step 5

The factors for $39$ are $1, 3, 13, 39$ .

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Step 5.1

The factors for $39$ are all numbers between $1$ and $39$ , which divide $39$ evenly.

Check numbers between $1$ and $39$

Step 5.2

Find the factor pairs of $39$ where $x \cdot y = 39$ .

$\begin{array}{c} x & y \\ 1 & 39 \\ 3 & 13 \end{array}$

Step 5.3

List the factors for $39$ .

$1, 3, 13, 39$

Step 6

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

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Step 6.1

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

Check numbers between $1$ and $48$

Step 6.2

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 6.3

List the factors for $48$ .

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

Step 7

The factors for $40$ are $1, 2, 4, 5, 8, 10, 20, 40$ .

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Step 7.1

The factors for $40$ are all numbers between $1$ and $40$ , which divide $40$ evenly.

Check numbers between $1$ and $40$

Step 7.2

Find the factor pairs of $40$ where $x \cdot y = 40$ .

$\begin{array}{c} x & y \\ 1 & 40 \\ 2 & 20 \\ 4 & 10 \\ 5 & 8 \end{array}$

Step 7.3

List the factors for $40$ .

$1, 2, 4, 5, 8, 10, 20, 40$

Step 8

The factors for $21$ are $1, 3, 7, 21$ .

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Step 8.1

The factors for $21$ are all numbers between $1$ and $21$ , which divide $21$ evenly.

Check numbers between $1$ and $21$

Step 8.2

Find the factor pairs of $21$ where $x \cdot y = 21$ .

$\begin{array}{c} x & y \\ 1 & 21 \\ 3 & 7 \end{array}$

Step 8.3

List the factors for $21$ .

$1, 3, 7, 21$

Step 9

List all the factors for $54, 45, 33, 39, 48, 40, 21$ to find the common factors.

$54$ : $1, 2, 3, 6, 9, 18, 27, 54$

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

$33$ : $1, 3, 11, 33$

$39$ : $1, 3, 13, 39$

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

$40$ : $1, 2, 4, 5, 8, 10, 20, 40$

$21$ : $1, 3, 7, 21$

Step 10

The common factors for $54, 45, 33, 39, 48, 40, 21$ are $1$ .

$1$

Step 11

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

$1$