Algebra Examples

16

$16$ ,

$24$ ,

$40$

Step 1

Find the common factors for the numerical part:

$16, 24, 40$

Step 2

The factors for

$16$ are

$1, 2, 4, 8, 16$ .

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Step 2.1

The factors for

$16$ are all numbers between

$1$ and

$16$ , which divide

$16$ evenly.

Check numbers between

$1$ and

$16$

Step 2.2

Find the factor pairs of

$16$ where

$x \cdot y = 16$ .

$\begin{array}{c} x & y \\ 1 & 16 \\ 2 & 8 \\ 4 & 4 \end{array}$

Step 2.3

List the factors for

$16$ .

$1, 2, 4, 8, 16$

Step 3

The factors for

$24$ are

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

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Step 3.1

The factors for

$24$ are all numbers between

$1$ and

$24$ , which divide

$24$ evenly.

Check numbers between

$1$ and

$24$

Step 3.2

Find the factor pairs of

$24$ where

$x \cdot y = 24$ .

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

Step 3.3

List the factors for

$24$ .

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

Step 4

The factors for

$40$ are

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

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Step 4.1

The factors for

$40$ are all numbers between

$1$ and

$40$ , which divide

$40$ evenly.

Check numbers between

$1$ and

$40$

Step 4.2

Find the factor pairs of

$40$ where

$x \cdot y = 40$ .

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

Step 4.3

List the factors for

$40$ .

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

Step 5

List all the factors for

$16, 24, 40$ to find the common factors.

$16$ :

$1, 2, 4, 8, 16$

$24$ :

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

$40$ :

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

Step 6

The common factors for

$16, 24, 40$ are

$1, 2, 4, 8$ .

$1, 2, 4, 8$

Step 7

The GCF (HCF) of the numerical factors

$1, 2, 4, 8$ is

$8$ .

$8$

$16, 24, 40$

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