Pre-Algebra Examples

$0$ ,

$1$ ,

$2$ ,

$3$ ,

$4$ ,

$5$ ,

$6$

Step 1

Find the common factors for the numerical part:

$0, 1, 2, 3, 4, 5, 6$

Step 2

Every number is a factor of

$0$ .

Infinitely many factors

Step 3

The factors for

$1$ are

$1$ .

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Step 3.1

The factors for

$1$ are all numbers between

$1$ and

$1$ , which divide

$1$ evenly.

Check numbers between

$1$ and

$1$

Step 3.2

Find the factor pairs of

$1$ where

$x \cdot y = 1$ .

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

Step 3.3

List the factors for

$1$ .

$1$

$1$

Step 4

The factors for

$2$ are

$1, 2$ .

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Step 4.1

The factors for

$2$ are all numbers between

$1$ and

$2$ , which divide

$2$ evenly.

Check numbers between

$1$ and

$2$

Step 4.2

Find the factor pairs of

$2$ where

$x \cdot y = 2$ .

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

Step 4.3

List the factors for

$2$ .

$1, 2$

$1, 2$

Step 5

The factors for

$3$ are

$1, 3$ .

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Step 5.1

The factors for

$3$ are all numbers between

$1$ and

$3$ , which divide

$3$ evenly.

Check numbers between

$1$ and

$3$

Step 5.2

Find the factor pairs of

$3$ where

$x \cdot y = 3$ .

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

Step 5.3

List the factors for

$3$ .

$1, 3$

$1, 3$

Step 6

The factors for

$4$ are

$1, 2, 4$ .

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Step 6.1

The factors for

$4$ are all numbers between

$1$ and

$4$ , which divide

$4$ evenly.

Check numbers between

$1$ and

$4$

Step 6.2

Find the factor pairs of

$4$ where

$x \cdot y = 4$ .

$\begin{array}{c} x & y \\ 1 & 4 \\ 2 & 2 \end{array}$

Step 6.3

List the factors for

$4$ .

$1, 2, 4$

$1, 2, 4$

Step 7

The factors for

$5$ are

$1, 5$ .

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Step 7.1

The factors for

$5$ are all numbers between

$1$ and

$5$ , which divide

$5$ evenly.

Check numbers between

$1$ and

$5$

Step 7.2

Find the factor pairs of

$5$ where

$x \cdot y = 5$ .

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

Step 7.3

List the factors for

$5$ .

$1, 5$

$1, 5$

Step 8

The factors for

$6$ are

$1, 2, 3, 6$ .

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Step 8.1

The factors for

$6$ are all numbers between

$1$ and

$6$ , which divide

$6$ evenly.

Check numbers between

$1$ and

$6$

Step 8.2

Find the factor pairs of

$6$ where

$x \cdot y = 6$ .

$\begin{array}{c} x & y \\ 1 & 6 \\ 2 & 3 \end{array}$

Step 8.3

List the factors for

$6$ .

$1, 2, 3, 6$

$1, 2, 3, 6$

Step 9

List all the factors for

$0, 1, 2, 3, 4, 5, 6$ to find the common factors.

$0$ : Infinitely many factors

$1$ :

$1$

$2$ :

$1, 2$

$3$ :

$1, 3$

$4$ :

$1, 2, 4$

$5$ :

$1, 5$

$6$ :

$1, 2, 3, 6$

Step 10

The common factors for

$0, 1, 2, 3, 4, 5, 6$ are

$1$ .

$1$

Step 11

The GCF (HCF) of the numerical factors

$1$ is

$1$ .

$1$

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