Algebra Examples

48

$48$ ,

72

$72$ ,

120

$120$

Step 1

Find the common factors for the numerical part:

48, 72, 120

$48, 72, 120$

Step 2

The factors for

48

$48$ are

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$ .

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Step 2.1

The factors for

48

$48$ are all numbers between

1

$1$ and

48

$48$ , which divide

48

$48$ evenly.

Check numbers between

1

$1$ and

48

$48$

Step 2.2

Find the factor pairs of

48

$48$ where

x \cdot y = 48

$x \cdot y = 48$ .

\begin{array}{c} x & y \\ 1 & 48 \\ 2 & 24 \\ 3 & 16 \\ 4 & 12 \\ 6 & 8 \end{array}

$\begin{array}{c} x & y \\ 1 & 48 \\ 2 & 24 \\ 3 & 16 \\ 4 & 12 \\ 6 & 8 \end{array}$

Step 2.3

List the factors for

48

$48$ .

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

Step 3

The factors for

72

$72$ are

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

$1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$ .

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Step 3.1

The factors for

72

$72$ are all numbers between

1

$1$ and

72

$72$ , which divide

72

$72$ evenly.

Check numbers between

1

$1$ and

72

$72$

Step 3.2

Find the factor pairs of

72

$72$ where

x \cdot y = 72

$x \cdot y = 72$ .

\begin{array}{c} x & y \\ 1 & 72 \\ 2 & 36 \\ 3 & 24 \\ 4 & 18 \\ 6 & 12 \\ 8 & 9 \end{array}

$\begin{array}{c} x & y \\ 1 & 72 \\ 2 & 36 \\ 3 & 24 \\ 4 & 18 \\ 6 & 12 \\ 8 & 9 \end{array}$

Step 3.3

List the factors for

72

$72$ .

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

$1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

$1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$

Step 4

The factors for

120

$120$ are

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

$1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$ .

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Step 4.1

The factors for

120

$120$ are all numbers between

1

$1$ and

120

$120$ , which divide

120

$120$ evenly.

Check numbers between

1

$1$ and

120

$120$

Step 4.2

Find the factor pairs of

120

$120$ where

x \cdot y = 120

$x \cdot y = 120$ .

\begin{array}{c} x & y \\ 1 & 120 \\ 2 & 60 \\ 3 & 40 \\ 4 & 30 \\ 5 & 24 \\ 6 & 20 \\ 8 & 15 \\ 10 & 12 \end{array}

$\begin{array}{c} x & y \\ 1 & 120 \\ 2 & 60 \\ 3 & 40 \\ 4 & 30 \\ 5 & 24 \\ 6 & 20 \\ 8 & 15 \\ 10 & 12 \end{array}$

Step 4.3

List the factors for

120

$120$ .

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

$1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

$1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$

Step 5

List all the factors for

48, 72, 120

$48, 72, 120$ to find the common factors.

48

$48$ :

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

$1, 2, 3, 4, 6, 8, 12, 16, 24, 48$

72

$72$ :

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

$1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72$

120

$120$ :

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

$1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120$

Step 6

The common factors for

48, 72, 120

$48, 72, 120$ are

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 7

The GCF (HCF) of the numerical factors

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

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

24

$24$ .

24

$24$