Pre-Algebra Examples

$67.94$ , $- 7.76$

Step 1

Convert all of the decimals to reduced fractions.

$\frac{3397}{50}, - \frac{194}{25}$

Step 2

Find the GCF for the numerators $3397, - 194$ .

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Step 2.1

Find the common factors for the numerical part:

$3397, - 194$

Step 2.2

The factors for $3397$ are $1, 43, 79, 3397$ .

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Step 2.2.1

The factors for $3397$ are all numbers between $1$ and $3397$ , which divide $3397$ evenly.

Check numbers between $1$ and $3397$

Step 2.2.2

Find the factor pairs of $3397$ where $x \cdot y = 3397$ .

$\begin{array}{c} x & y \\ 1 & 3397 \\ 43 & 79 \end{array}$

Step 2.2.3

List the factors for $3397$ .

$1, 43, 79, 3397$

Step 2.3

The factors for $- 194$ are $1, 2, 97, 194$ .

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Step 2.3.1

The factors for $- 194$ are all numbers between $1$ and $194$ , which divide $- 194$ evenly.

Check numbers between $1$ and $194$

Step 2.3.2

Find the factor pairs of $- 194$ where $x \cdot y = - 194$ .

$\begin{array}{c} x & y \\ 1 & 194 \\ 2 & 97 \end{array}$

Step 2.3.3

List the factors for $- 194$ .

$1, 2, 97, 194$

Step 2.4

List all the factors for $3397, - 194$ to find the common factors.

$3397$ : $1, 43, 79, 3397$

$- 194$ : $1, 2, 97, 194$

Step 2.5

The common factors for $3397, - 194$ are $1$ .

$1$

Step 2.6

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

$1$

Step 3

Find the GCF for the denominators $50, 25$ .

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Step 3.1

Find the common factors for the numerical part:

$50, 25$

Step 3.2

The factors for $50$ are $1, 2, 5, 10, 25, 50$ .

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Step 3.2.1

The factors for $50$ are all numbers between $1$ and $50$ , which divide $50$ evenly.

Check numbers between $1$ and $50$

Step 3.2.2

Find the factor pairs of $50$ where $x \cdot y = 50$ .

$\begin{array}{c} x & y \\ 1 & 50 \\ 2 & 25 \\ 5 & 10 \end{array}$

Step 3.2.3

List the factors for $50$ .

$1, 2, 5, 10, 25, 50$

Step 3.3

The factors for $25$ are $1, 5, 25$ .

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Step 3.3.1

The factors for $25$ are all numbers between $1$ and $25$ , which divide $25$ evenly.

Check numbers between $1$ and $25$

Step 3.3.2

Find the factor pairs of $25$ where $x \cdot y = 25$ .

$\begin{array}{c} x & y \\ 1 & 25 \\ 5 & 5 \end{array}$

Step 3.3.3

List the factors for $25$ .

$1, 5, 25$

Step 3.4

List all the factors for $50, 25$ to find the common factors.

$50$ : $1, 2, 5, 10, 25, 50$

$25$ : $1, 5, 25$

Step 3.5

The common factors for $50, 25$ are $1, 5, 25$ .

$1, 5, 25$

Step 3.6

The GCF (HCF) of the numerical factors $1, 5, 25$ is $25$ .

$25$

Step 4

Determine the GCF for $\frac{3397}{50}, - \frac{194}{25}$ .

$\frac{1}{25}$

Step 5

Convert the GCF $\frac{1}{25}$ to decimal.

$0.04$