Algebra Examples

81

$81$ ,

90

$90$ ,

99

$99$

Step 1

Find the common factors for the numerical part:

81, 90, 99

$81, 90, 99$

Step 2

The factors for

81

$81$ are

1, 3, 9, 27, 81

$1, 3, 9, 27, 81$ .

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Step 2.1

The factors for

81

$81$ are all numbers between

1

$1$ and

81

$81$ , which divide

81

$81$ evenly.

Check numbers between

1

$1$ and

81

$81$

Step 2.2

Find the factor pairs of

81

$81$ where

x \cdot y = 81

$x \cdot y = 81$ .

\begin{matrix} x & y 1 & 81 3 & 27 9 & 9 \end{matrix}

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

Step 2.3

List the factors for

81

$81$ .

1, 3, 9, 27, 81

$1, 3, 9, 27, 81$

1, 3, 9, 27, 81

$1, 3, 9, 27, 81$

Step 3

The factors for

90

$90$ are

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

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

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Step 3.1

The factors for

90

$90$ are all numbers between

1

$1$ and

90

$90$ , which divide

90

$90$ evenly.

Check numbers between

1

$1$ and

90

$90$

Step 3.2

Find the factor pairs of

90

$90$ where

x \cdot y = 90

$x \cdot y = 90$ .

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

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

Step 3.3

List the factors for

90

$90$ .

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

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

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

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

Step 4

The factors for

99

$99$ are

1, 3, 9, 11, 33, 99

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

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Step 4.1

The factors for

99

$99$ are all numbers between

1

$1$ and

99

$99$ , which divide

99

$99$ evenly.

Check numbers between

1

$1$ and

99

$99$

Step 4.2

Find the factor pairs of

99

$99$ where

x \cdot y = 99

$x \cdot y = 99$ .

\begin{matrix} x & y 1 & 99 3 & 33 9 & 11 \end{matrix}

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

Step 4.3

List the factors for

99

$99$ .

1, 3, 9, 11, 33, 99

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

1, 3, 9, 11, 33, 99

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

Step 5

List all the factors for

81, 90, 99

$81, 90, 99$ to find the common factors.

81

$81$ :

1, 3, 9, 27, 81

$1, 3, 9, 27, 81$

90

$90$ :

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

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

99

$99$ :

1, 3, 9, 11, 33, 99

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

Step 6

The common factors for

81, 90, 99

$81, 90, 99$ are

1, 3, 9

$1, 3, 9$ .

1, 3, 9

$1, 3, 9$

Step 7

The GCF (HCF) of the numerical factors

1, 3, 9

$1, 3, 9$ is

9

$9$ .

9

$9$

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