Algebra Examples

28

$28$ ,

20

$20$ ,

40

$40$

Step 1

Find the common factors for the numerical part:

28, 20, 40

$28, 20, 40$

Step 2

The factors for

28

$28$ are

1, 2, 4, 7, 14, 28

$1, 2, 4, 7, 14, 28$ .

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Step 2.1

The factors for

28

$28$ are all numbers between

1

$1$ and

28

$28$ , which divide

28

$28$ evenly.

Check numbers between

1

$1$ and

28

$28$

Step 2.2

Find the factor pairs of

28

$28$ where

x \cdot y = 28

$x \cdot y = 28$ .

\begin{array}{c} x & y \\ 1 & 28 \\ 2 & 14 \\ 4 & 7 \end{array}

$\begin{array}{c} x & y \\ 1 & 28 \\ 2 & 14 \\ 4 & 7 \end{array}$

Step 2.3

List the factors for

28

$28$ .

1, 2, 4, 7, 14, 28

$1, 2, 4, 7, 14, 28$

1, 2, 4, 7, 14, 28

$1, 2, 4, 7, 14, 28$

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

40

$40$ are

1, 2, 4, 5, 8, 10, 20, 40

$1, 2, 4, 5, 8, 10, 20, 40$ .

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Step 4.1

The factors for

40

$40$ are all numbers between

1

$1$ and

40

$40$ , which divide

40

$40$ evenly.

Check numbers between

1

$1$ and

40

$40$

Step 4.2

Find the factor pairs of

40

$40$ where

x \cdot y = 40

$x \cdot y = 40$ .

\begin{array}{c} x & y \\ 1 & 40 \\ 2 & 20 \\ 4 & 10 \\ 5 & 8 \end{array}

$\begin{array}{c} x & y \\ 1 & 40 \\ 2 & 20 \\ 4 & 10 \\ 5 & 8 \end{array}$

Step 4.3

List the factors for

40

$40$ .

1, 2, 4, 5, 8, 10, 20, 40

$1, 2, 4, 5, 8, 10, 20, 40$

1, 2, 4, 5, 8, 10, 20, 40

$1, 2, 4, 5, 8, 10, 20, 40$

Step 5

List all the factors for

28, 20, 40

$28, 20, 40$ to find the common factors.

28

$28$ :

1, 2, 4, 7, 14, 28

$1, 2, 4, 7, 14, 28$

20

$20$ :

1, 2, 4, 5, 10, 20

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

40

$40$ :

1, 2, 4, 5, 8, 10, 20, 40

$1, 2, 4, 5, 8, 10, 20, 40$

Step 6

The common factors for

28, 20, 40

$28, 20, 40$ 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

$4$