Algebra Examples

7

$7$ ,

15

$15$ ,

21

$21$

Step 1

Find the common factors for the numerical part:

7, 15, 21

$7, 15, 21$

Step 2

The factors for

7

$7$ are

1, 7

$1, 7$ .

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Step 2.1

The factors for

7

$7$ are all numbers between

1

$1$ and

7

$7$ , which divide

7

$7$ evenly.

Check numbers between

1

$1$ and

7

$7$

Step 2.2

Find the factor pairs of

7

$7$ where

x \cdot y = 7

$x \cdot y = 7$ .

\begin{matrix} x & y 1 & 7 \end{matrix}

$\begin{array}{c} x & y \\ 1 & 7 \end{array}$

Step 2.3

List the factors for

7

$7$ .

1, 7

$1, 7$

1, 7

$1, 7$

Step 3

The factors for

15

$15$ are

1, 3, 5, 15

$1, 3, 5, 15$ .

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Step 3.1

The factors for

15

$15$ are all numbers between

1

$1$ and

15

$15$ , which divide

15

$15$ evenly.

Check numbers between

1

$1$ and

15

$15$

Step 3.2

Find the factor pairs of

15

$15$ where

x \cdot y = 15

$x \cdot y = 15$ .

\begin{matrix} x & y 1 & 15 3 & 5 \end{matrix}

$\begin{array}{c} x & y \\ 1 & 15 \\ 3 & 5 \end{array}$

Step 3.3

List the factors for

15

$15$ .

1, 3, 5, 15

$1, 3, 5, 15$

1, 3, 5, 15

$1, 3, 5, 15$

Step 4

The factors for

21

$21$ are

1, 3, 7, 21

$1, 3, 7, 21$ .

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Step 4.1

The factors for

$21$ are all numbers between

$1$ and

$21$ , which divide

$21$ evenly.

Check numbers between

$1$ and

$21$

Step 4.2

Find the factor pairs of

$21$ where

$x \cdot y = 21$ .

$\begin{array}{c} x & y \\ 1 & 21 \\ 3 & 7 \end{array}$

Step 4.3

List the factors for

$21$ .

$1, 3, 7, 21$

$1, 3, 7, 21$

Step 5

List all the factors for

$7, 15, 21$ to find the common factors.

$7$ :

$1, 7$

$15$ :

$1, 3, 5, 15$

$21$ :

$1, 3, 7, 21$

Step 6

The common factors for

$7, 15, 21$ are

$1$ .

$1$

Step 7

The GCF (HCF) of the numerical factors

$1$ is

$1$ .

$1$

$7, 15, 21$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$