Algebra Examples

10

$10$ ,

25

$25$

Step 1

Find the common factors for the numerical part:

10, 25

$10, 25$

Step 2

The factors for

10

$10$ are

1, 2, 5, 10

$1, 2, 5, 10$ .

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Step 2.1

The factors for

10

$10$ are all numbers between

1

$1$ and

10

$10$ , which divide

10

$10$ evenly.

Check numbers between

1

$1$ and

10

$10$

Step 2.2

Find the factor pairs of

10

$10$ where

x \cdot y = 10

$x \cdot y = 10$ .

\begin{array}{c} x & y \\ 1 & 10 \\ 2 & 5 \end{array}

$\begin{array}{c} x & y \\ 1 & 10 \\ 2 & 5 \end{array}$

Step 2.3

List the factors for

10

$10$ .

1, 2, 5, 10

$1, 2, 5, 10$

1, 2, 5, 10

$1, 2, 5, 10$

Step 3

The factors for

25

$25$ are

1, 5, 25

$1, 5, 25$ .

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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

List all the factors for

10, 25

$10, 25$ to find the common factors.

10

$10$ :

1, 2, 5, 10

$1, 2, 5, 10$

25

$25$ :

1, 5, 25

$1, 5, 25$

Step 5

The common factors for

10, 25

$10, 25$ are

1, 5

$1, 5$ .

1, 5

$1, 5$

Step 6

The GCF (HCF) of the numerical factors

1, 5

$1, 5$ is

5

$5$ .

5

$5$

10, 25

$10, 25$

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