Algebra Examples

30

$30$ ,

48

$48$

Step 1

Find the common factors for the numerical part:

30, 48

$30, 48$

Step 2

The factors for

30

$30$ are

1, 2, 3, 5, 6, 10, 15, 30

$1, 2, 3, 5, 6, 10, 15, 30$ .

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Step 2.1

The factors for

30

$30$ are all numbers between

1

$1$ and

30

$30$ , which divide

30

$30$ evenly.

Check numbers between

1

$1$ and

30

$30$

Step 2.2

Find the factor pairs of

30

$30$ where

x \cdot y = 30

$x \cdot y = 30$ .

\begin{array}{c} x & y \\ 1 & 30 \\ 2 & 15 \\ 3 & 10 \\ 5 & 6 \end{array}

$\begin{array}{c} x & y \\ 1 & 30 \\ 2 & 15 \\ 3 & 10 \\ 5 & 6 \end{array}$

Step 2.3

List the factors for

30

$30$ .

1, 2, 3, 5, 6, 10, 15, 30

$1, 2, 3, 5, 6, 10, 15, 30$

1, 2, 3, 5, 6, 10, 15, 30

$1, 2, 3, 5, 6, 10, 15, 30$

Step 3

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 3.1

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 3.2

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 3.3

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 4

List all the factors for

30, 48

$30, 48$ to find the common factors.

30

$30$ :

1, 2, 3, 5, 6, 10, 15, 30

$1, 2, 3, 5, 6, 10, 15, 30$

48

$48$ :

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

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

Step 5

The common factors for

30, 48

$30, 48$ are

1, 2, 3, 6

$1, 2, 3, 6$ .

1, 2, 3, 6

$1, 2, 3, 6$

Step 6

The GCF (HCF) of the numerical factors

1, 2, 3, 6

$1, 2, 3, 6$ is

6

$6$ .

6

$6$