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 $1$ .

$1$

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 $2$ .

$1, 2$

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 $3$ .

$1, 3$

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 $4$ .

$1, 2, 4$

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 $5$ .

$1, 5$

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 $6$ .

$1, 2, 3, 6$

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 $1$ .

$1$