Pre-Algebra Examples

11

$11$ ,

13

$13$ ,

5

$5$ ,

15

$15$ ,

14

$14$

Step 1

Find the common factors for the numerical part:

11, 13, 5, 15, 14

$11, 13, 5, 15, 14$

Step 2

The factors for

11

$11$ are

1, 11

$1, 11$ .

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Step 2.1

The factors for

11

$11$ are all numbers between

1

$1$ and

11

$11$ , which divide

11

$11$ evenly.

Check numbers between

1

$1$ and

11

$11$

Step 2.2

Find the factor pairs of

11

$11$ where

x \cdot y = 11

$x \cdot y = 11$ .

\begin{matrix} x & y 1 & 11 \end{matrix}

$\begin{array}{c} x & y \\ 1 & 11 \end{array}$

Step 2.3

List the factors for

11

$11$ .

1, 11

$1, 11$

1, 11

$1, 11$

Step 3

The factors for

13

$13$ are

1, 13

$1, 13$ .

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Step 3.1

The factors for

13

$13$ are all numbers between

1

$1$ and

13

$13$ , which divide

13

$13$ evenly.

Check numbers between

1

$1$ and

13

$13$

Step 3.2

Find the factor pairs of

13

$13$ where

x \cdot y = 13

$x \cdot y = 13$ .

\begin{matrix} x & y 1 & 13 \end{matrix}

$\begin{array}{c} x & y \\ 1 & 13 \end{array}$

Step 3.3

List the factors for

13

$13$ .

1, 13

$1, 13$

1, 13

$1, 13$

Step 4

The factors for

5

$5$ are

1, 5

$1, 5$ .

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Step 4.1

The factors for

5

$5$ are all numbers between

1

$1$ and

5

$5$ , which divide

5

$5$ evenly.

Check numbers between

1

$1$ and

5

$5$

Step 4.2

Find the factor pairs of

5

$5$ where

x \cdot y = 5

$x \cdot y = 5$ .

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

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

Step 4.3

List the factors for

5

$5$ .

1, 5

$1, 5$

1, 5

$1, 5$

Step 5

The factors for

15

$15$ are

1, 3, 5, 15

$1, 3, 5, 15$ .

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Step 5.1

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 5.2

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 5.3

List the factors for

15

$15$ .

1, 3, 5, 15

$1, 3, 5, 15$

1, 3, 5, 15

$1, 3, 5, 15$

Step 6

The factors for

14

$14$ are

1, 2, 7, 14

$1, 2, 7, 14$ .

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Step 6.1

The factors for

14

$14$ are all numbers between

1

$1$ and

14

$14$ , which divide

14

$14$ evenly.

Check numbers between

1

$1$ and

14

$14$

Step 6.2

Find the factor pairs of

14

$14$ where

x \cdot y = 14

$x \cdot y = 14$ .

\begin{matrix} x & y 1 & 14 2 & 7 \end{matrix}

$\begin{array}{c} x & y \\ 1 & 14 \\ 2 & 7 \end{array}$

Step 6.3

List the factors for

14

$14$ .

1, 2, 7, 14

$1, 2, 7, 14$

1, 2, 7, 14

$1, 2, 7, 14$

Step 7

List all the factors for

11, 13, 5, 15, 14

$11, 13, 5, 15, 14$ to find the common factors.

11

$11$ :

1, 11

$1, 11$

13

$13$ :

1, 13

$1, 13$

5

$5$ :

1, 5

$1, 5$

15

$15$ :

1, 3, 5, 15

$1, 3, 5, 15$

14

$14$ :

1, 2, 7, 14

$1, 2, 7, 14$

Step 8

The common factors for

11, 13, 5, 15, 14

$11, 13, 5, 15, 14$ are

1

$1$ .

1

$1$

Step 9

The GCF (HCF) of the numerical factors

1

$1$ is

1

$1$ .

1

$1$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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