Examples

5

$5$ ,

25

$25$ ,

125

$125$

Step 1

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

Step 2

Find the factors of

5

$5$ .

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Step 2.1

The factors for

5

$5$ are all numbers between

1

$1$ and

5

$5$ , which divide

5

$5$ evenly.

Check numbers between

1

$1$ and

5

$5$

Step 2.2

Find the factor pairs of

5

$5$ where

x \cdot y = 5

$x \cdot y = 5$ .

\begin{array}{c} x & y \\ 1 & 5 \end{array}

$\begin{array}{c} x & y \\ 1 & 5 \end{array}$

Step 2.3

List the factors for

5

$5$ .

1, 5

$1, 5$

1, 5

$1, 5$

Step 3

Find the factors of

25

$25$ .

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Step 3.1

The factors for

25

$25$ are all numbers between

1

$1$ and

25

$25$ , which divide

25

$25$ evenly.

Check numbers between

1

$1$ and

25

$25$

Step 3.2

Find the factor pairs of

25

$25$ where

x \cdot y = 25

$x \cdot y = 25$ .

\begin{array}{c} x & y \\ 1 & 25 \\ 5 & 5 \end{array}

$\begin{array}{c} x & y \\ 1 & 25 \\ 5 & 5 \end{array}$

Step 3.3

List the factors for

25

$25$ .

1, 5, 25

$1, 5, 25$

1, 5, 25

$1, 5, 25$

Step 4

Find the factors of

125

$125$ .

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Step 4.1

The factors for

125

$125$ are all numbers between

1

$1$ and

125

$125$ , which divide

125

$125$ evenly.

Check numbers between

1

$1$ and

125

$125$

Step 4.2

Find the factor pairs of

125

$125$ where

x \cdot y = 125

$x \cdot y = 125$ .

\begin{array}{c} x & y \\ 1 & 125 \\ 5 & 25 \end{array}

$\begin{array}{c} x & y \\ 1 & 125 \\ 5 & 25 \end{array}$

Step 4.3

List the factors for

125

$125$ .

1, 5, 25, 125

$1, 5, 25, 125$

1, 5, 25, 125

$1, 5, 25, 125$

Step 5

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

1, 5

$1, 5$

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