Algebra Examples

12

$12$ ,

20

$20$ ,

24

$24$

Step 1

Find the common factors for the numerical part:

12, 20, 24

$12, 20, 24$

Step 2

The factors for

12

$12$ are

1, 2, 3, 4, 6, 12

$1, 2, 3, 4, 6, 12$ .

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Step 2.1

The factors for

12

$12$ are all numbers between

1

$1$ and

12

$12$ , which divide

12

$12$ evenly.

Check numbers between

1

$1$ and

12

$12$

Step 2.2

Find the factor pairs of

12

$12$ where

x \cdot y = 12

$x \cdot y = 12$ .

\begin{array}{c} x & y \\ 1 & 12 \\ 2 & 6 \\ 3 & 4 \end{array}

$\begin{array}{c} x & y \\ 1 & 12 \\ 2 & 6 \\ 3 & 4 \end{array}$

Step 2.3

List the factors for

12

$12$ .

1, 2, 3, 4, 6, 12

$1, 2, 3, 4, 6, 12$

1, 2, 3, 4, 6, 12

$1, 2, 3, 4, 6, 12$

Step 3

The factors for

20

$20$ are

1, 2, 4, 5, 10, 20

$1, 2, 4, 5, 10, 20$ .

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Step 3.1

The factors for

20

$20$ are all numbers between

1

$1$ and

20

$20$ , which divide

20

$20$ evenly.

Check numbers between

1

$1$ and

20

$20$

Step 3.2

Find the factor pairs of

20

$20$ where

x \cdot y = 20

$x \cdot y = 20$ .

\begin{array}{c} x & y \\ 1 & 20 \\ 2 & 10 \\ 4 & 5 \end{array}

$\begin{array}{c} x & y \\ 1 & 20 \\ 2 & 10 \\ 4 & 5 \end{array}$

Step 3.3

List the factors for

20

$20$ .

1, 2, 4, 5, 10, 20

$1, 2, 4, 5, 10, 20$

1, 2, 4, 5, 10, 20

$1, 2, 4, 5, 10, 20$

Step 4

The factors for

24

$24$ are

1, 2, 3, 4, 6, 8, 12, 24

$1, 2, 3, 4, 6, 8, 12, 24$ .

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Step 4.1

The factors for

24

$24$ are all numbers between

1

$1$ and

24

$24$ , which divide

24

$24$ evenly.

Check numbers between

1

$1$ and

24

$24$

Step 4.2

Find the factor pairs of

24

$24$ where

x \cdot y = 24

$x \cdot y = 24$ .

\begin{array}{c} x & y \\ 1 & 24 \\ 2 & 12 \\ 3 & 8 \\ 4 & 6 \end{array}

$\begin{array}{c} x & y \\ 1 & 24 \\ 2 & 12 \\ 3 & 8 \\ 4 & 6 \end{array}$

Step 4.3

List the factors for

24

$24$ .

1, 2, 3, 4, 6, 8, 12, 24

$1, 2, 3, 4, 6, 8, 12, 24$

1, 2, 3, 4, 6, 8, 12, 24

$1, 2, 3, 4, 6, 8, 12, 24$

Step 5

List all the factors for

12, 20, 24

$12, 20, 24$ to find the common factors.

12

$12$ :

1, 2, 3, 4, 6, 12

$1, 2, 3, 4, 6, 12$

20

$20$ :

1, 2, 4, 5, 10, 20

$1, 2, 4, 5, 10, 20$

24

$24$ :

1, 2, 3, 4, 6, 8, 12, 24

$1, 2, 3, 4, 6, 8, 12, 24$

Step 6

The common factors for

12, 20, 24

$12, 20, 24$ are

1, 2, 4

$1, 2, 4$ .

1, 2, 4

$1, 2, 4$

Step 7

The GCF (HCF) of the numerical factors

1, 2, 4

$1, 2, 4$ is

4

$4$ .

4

$4$