Algebra Examples

$81$ , $90$ , $99$

Step 1

Find the common factors for the numerical part:

$81, 90, 99$

Step 2

The factors for $81$ are $1, 3, 9, 27, 81$ .

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Step 2.1

The factors for $81$ are all numbers between $1$ and $81$ , which divide $81$ evenly.

Check numbers between $1$ and $81$

Step 2.2

Find the factor pairs of $81$ where $x \cdot y = 81$ .

$\begin{array}{c} x & y \\ 1 & 81 \\ 3 & 27 \\ 9 & 9 \end{array}$

Step 2.3

List the factors for $81$ .

$1, 3, 9, 27, 81$

Step 3

The factors for $90$ are $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$ .

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Step 3.1

The factors for $90$ are all numbers between $1$ and $90$ , which divide $90$ evenly.

Check numbers between $1$ and $90$

Step 3.2

Find the factor pairs of $90$ where $x \cdot y = 90$ .

$\begin{array}{c} x & y \\ 1 & 90 \\ 2 & 45 \\ 3 & 30 \\ 5 & 18 \\ 6 & 15 \\ 9 & 10 \end{array}$

Step 3.3

List the factors for $90$ .

$1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

Step 4

The factors for $99$ are $1, 3, 9, 11, 33, 99$ .

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Step 4.1

The factors for $99$ are all numbers between $1$ and $99$ , which divide $99$ evenly.

Check numbers between $1$ and $99$

Step 4.2

Find the factor pairs of $99$ where $x \cdot y = 99$ .

$\begin{array}{c} x & y \\ 1 & 99 \\ 3 & 33 \\ 9 & 11 \end{array}$

Step 4.3

List the factors for $99$ .

$1, 3, 9, 11, 33, 99$

Step 5

List all the factors for $81, 90, 99$ to find the common factors.

$81$ : $1, 3, 9, 27, 81$

$90$ : $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

$99$ : $1, 3, 9, 11, 33, 99$

Step 6

The common factors for $81, 90, 99$ are $1, 3, 9$ .

$1, 3, 9$

Step 7

The GCF (HCF) of the numerical factors $1, 3, 9$ is $9$ .

$9$

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