Examples

45

$45$ ,

90

$90$

Step 1

To find the common factors of a list of numbers, find the factors of each number.

Step 2

Find the factors of

45

$45$ .

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Step 2.1

The factors for

45

$45$ are all numbers between

1

$1$ and

45

$45$ , which divide

45

$45$ evenly.

Check numbers between

1

$1$ and

45

$45$

Step 2.2

Find the factor pairs of

45

$45$ where

x \cdot y = 45

$x \cdot y = 45$ .

\begin{matrix} x & y 1 & 45 3 & 15 5 & 9 \end{matrix}

$\begin{array}{c} x & y \\ 1 & 45 \\ 3 & 15 \\ 5 & 9 \end{array}$

Step 2.3

List the factors for

45

$45$ .

1, 3, 5, 9, 15, 45

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

1, 3, 5, 9, 15, 45

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

Step 3

Find the factors of

90

$90$ .

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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 common factors are the ones that appear in the list of factors of each number.

1, 3, 5, 9, 15, 45

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

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