Algebra Examples

30

$30$ ,

42

$42$ ,

60

$60$ ,

48

$48$

Step 1

Find the common factors for the numerical part:

30, 42, 60, 48

$30, 42, 60, 48$

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{matrix} x & y 1 & 30 2 & 15 3 & 10 5 & 6 \end{matrix}

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

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

42

$42$ are

1, 2, 3, 6, 7, 14, 21, 42

$1, 2, 3, 6, 7, 14, 21, 42$ .

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Step 3.1

The factors for

42

$42$ are all numbers between

1

$1$ and

42

$42$ , which divide

42

$42$ evenly.

Check numbers between

1

$1$ and

42

$42$

Step 3.2

Find the factor pairs of

42

$42$ where

x \cdot y = 42

$x \cdot y = 42$ .

\begin{matrix} x & y 1 & 42 2 & 21 3 & 14 6 & 7 \end{matrix}

$\begin{array}{c} x & y \\ 1 & 42 \\ 2 & 21 \\ 3 & 14 \\ 6 & 7 \end{array}$

Step 3.3

List the factors for

42

$42$ .

1, 2, 3, 6, 7, 14, 21, 42

$1, 2, 3, 6, 7, 14, 21, 42$

1, 2, 3, 6, 7, 14, 21, 42

$1, 2, 3, 6, 7, 14, 21, 42$

Step 4

The factors for

60

$60$ are

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$ .

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Step 4.1

The factors for

60

$60$ are all numbers between

1

$1$ and

60

$60$ , which divide

60

$60$ evenly.

Check numbers between

1

$1$ and

60

$60$

Step 4.2

Find the factor pairs of

60

$60$ where

x \cdot y = 60

$x \cdot y = 60$ .

\begin{matrix} x & y 1 & 60 2 & 30 3 & 20 4 & 15 5 & 12 6 & 10 \end{matrix}

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

Step 4.3

List the factors for

60

$60$ .

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

Step 5

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 5.1

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 5.2

Find the factor pairs of

48

$48$ where

x \cdot y = 48

$x \cdot y = 48$ .

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

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

Step 5.3

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 6

List all the factors for

30, 42, 60, 48

$30, 42, 60, 48$ to find the common factors.

30

$30$ :

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

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

42

$42$ :

1, 2, 3, 6, 7, 14, 21, 42

$1, 2, 3, 6, 7, 14, 21, 42$

60

$60$ :

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

48

$48$ :

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

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

Step 7

The common factors for

30, 42, 60, 48

$30, 42, 60, 48$ are

1, 2, 3, 6

$1, 2, 3, 6$ .

1, 2, 3, 6

$1, 2, 3, 6$

Step 8

The GCF (HCF) of the numerical factors

1, 2, 3, 6

$1, 2, 3, 6$ is

6

$6$ .

6

$6$