Pre-Algebra Examples

$209$ , $210$ , $212$ , $214$ , $215$ , $217$ , $218$ , $219$ , $220$ , $221$ , $222$ , $223$ , $224$

Step 1

Find the common factors for the numerical part:

$209, 210, 212, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224$

Step 2

The factors for $209$ are $1, 11, 19, 209$ .

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Step 2.1

The factors for $209$ are all numbers between $1$ and $209$ , which divide $209$ evenly.

Check numbers between $1$ and $209$

Step 2.2

Find the factor pairs of $209$ where $x \cdot y = 209$ .

$\begin{array}{c} x & y \\ 1 & 209 \\ 11 & 19 \end{array}$

Step 2.3

List the factors for $209$ .

$1, 11, 19, 209$

Step 3

The factors for $210$ are $1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210$ .

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Step 3.1

The factors for $210$ are all numbers between $1$ and $210$ , which divide $210$ evenly.

Check numbers between $1$ and $210$

Step 3.2

Find the factor pairs of $210$ where $x \cdot y = 210$ .

$\begin{array}{c} x & y \\ 1 & 210 \\ 2 & 105 \\ 3 & 70 \\ 5 & 42 \\ 6 & 35 \\ 7 & 30 \\ 10 & 21 \\ 14 & 15 \end{array}$

Step 3.3

List the factors for $210$ .

$1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210$

Step 4

The factors for $212$ are $1, 2, 4, 53, 106, 212$ .

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Step 4.1

The factors for $212$ are all numbers between $1$ and $212$ , which divide $212$ evenly.

Check numbers between $1$ and $212$

Step 4.2

Find the factor pairs of $212$ where $x \cdot y = 212$ .

$\begin{array}{c} x & y \\ 1 & 212 \\ 2 & 106 \\ 4 & 53 \end{array}$

Step 4.3

List the factors for $212$ .

$1, 2, 4, 53, 106, 212$

Step 5

The factors for $214$ are $1, 2, 107, 214$ .

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Step 5.1

The factors for $214$ are all numbers between $1$ and $214$ , which divide $214$ evenly.

Check numbers between $1$ and $214$

Step 5.2

Find the factor pairs of $214$ where $x \cdot y = 214$ .

$\begin{array}{c} x & y \\ 1 & 214 \\ 2 & 107 \end{array}$

Step 5.3

List the factors for $214$ .

$1, 2, 107, 214$

Step 6

The factors for $215$ are $1, 5, 43, 215$ .

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Step 6.1

The factors for $215$ are all numbers between $1$ and $215$ , which divide $215$ evenly.

Check numbers between $1$ and $215$

Step 6.2

Find the factor pairs of $215$ where $x \cdot y = 215$ .

$\begin{array}{c} x & y \\ 1 & 215 \\ 5 & 43 \end{array}$

Step 6.3

List the factors for $215$ .

$1, 5, 43, 215$

Step 7

The factors for $217$ are $1, 7, 31, 217$ .

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Step 7.1

The factors for $217$ are all numbers between $1$ and $217$ , which divide $217$ evenly.

Check numbers between $1$ and $217$

Step 7.2

Find the factor pairs of $217$ where $x \cdot y = 217$ .

$\begin{array}{c} x & y \\ 1 & 217 \\ 7 & 31 \end{array}$

Step 7.3

List the factors for $217$ .

$1, 7, 31, 217$

Step 8

The factors for $218$ are $1, 2, 109, 218$ .

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Step 8.1

The factors for $218$ are all numbers between $1$ and $218$ , which divide $218$ evenly.

Check numbers between $1$ and $218$

Step 8.2

Find the factor pairs of $218$ where $x \cdot y = 218$ .

$\begin{array}{c} x & y \\ 1 & 218 \\ 2 & 109 \end{array}$

Step 8.3

List the factors for $218$ .

$1, 2, 109, 218$

Step 9

The factors for $219$ are $1, 3, 73, 219$ .

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Step 9.1

The factors for $219$ are all numbers between $1$ and $219$ , which divide $219$ evenly.

Check numbers between $1$ and $219$

Step 9.2

Find the factor pairs of $219$ where $x \cdot y = 219$ .

$\begin{array}{c} x & y \\ 1 & 219 \\ 3 & 73 \end{array}$

Step 9.3

List the factors for $219$ .

$1, 3, 73, 219$

Step 10

The factors for $220$ are $1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220$ .

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Step 10.1

The factors for $220$ are all numbers between $1$ and $220$ , which divide $220$ evenly.

Check numbers between $1$ and $220$

Step 10.2

Find the factor pairs of $220$ where $x \cdot y = 220$ .

$\begin{array}{c} x & y \\ 1 & 220 \\ 2 & 110 \\ 4 & 55 \\ 5 & 44 \\ 10 & 22 \\ 11 & 20 \end{array}$

Step 10.3

List the factors for $220$ .

$1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220$

Step 11

The factors for $221$ are $1, 13, 17, 221$ .

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Step 11.1

The factors for $221$ are all numbers between $1$ and $221$ , which divide $221$ evenly.

Check numbers between $1$ and $221$

Step 11.2

Find the factor pairs of $221$ where $x \cdot y = 221$ .

$\begin{array}{c} x & y \\ 1 & 221 \\ 13 & 17 \end{array}$

Step 11.3

List the factors for $221$ .

$1, 13, 17, 221$

Step 12

The factors for $222$ are $1, 2, 3, 6, 37, 74, 111, 222$ .

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Step 12.1

The factors for $222$ are all numbers between $1$ and $222$ , which divide $222$ evenly.

Check numbers between $1$ and $222$

Step 12.2

Find the factor pairs of $222$ where $x \cdot y = 222$ .

$\begin{array}{c} x & y \\ 1 & 222 \\ 2 & 111 \\ 3 & 74 \\ 6 & 37 \end{array}$

Step 12.3

List the factors for $222$ .

$1, 2, 3, 6, 37, 74, 111, 222$

Step 13

The factors for $223$ are $1, 223$ .

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Step 13.1

The factors for $223$ are all numbers between $1$ and $223$ , which divide $223$ evenly.

Check numbers between $1$ and $223$

Step 13.2

Find the factor pairs of $223$ where $x \cdot y = 223$ .

$\begin{array}{c} x & y \\ 1 & 223 \end{array}$

Step 13.3

List the factors for $223$ .

$1, 223$

Step 14

The factors for $224$ are $1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224$ .

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Step 14.1

The factors for $224$ are all numbers between $1$ and $224$ , which divide $224$ evenly.

Check numbers between $1$ and $224$

Step 14.2

Find the factor pairs of $224$ where $x \cdot y = 224$ .

$\begin{array}{c} x & y \\ 1 & 224 \\ 2 & 112 \\ 4 & 56 \\ 7 & 32 \\ 8 & 28 \\ 14 & 16 \end{array}$

Step 14.3

List the factors for $224$ .

$1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224$

Step 15

List all the factors for $209, 210, 212, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224$ to find the common factors.

$209$ : $1, 11, 19, 209$

$210$ : $1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210$

$212$ : $1, 2, 4, 53, 106, 212$

$214$ : $1, 2, 107, 214$

$215$ : $1, 5, 43, 215$

$217$ : $1, 7, 31, 217$

$218$ : $1, 2, 109, 218$

$219$ : $1, 3, 73, 219$

$220$ : $1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220$

$221$ : $1, 13, 17, 221$

$222$ : $1, 2, 3, 6, 37, 74, 111, 222$

$223$ : $1, 223$

$224$ : $1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224$

Step 16

The common factors for $209, 210, 212, 214, 215, 217, 218, 219, 220, 221, 222, 223, 224$ are $1$ .

$1$

Step 17

The GCF (HCF) of the numerical factors $1$ is $1$ .

$1$