Pre-Algebra Examples

$300$ , $125$

Step 1

Find the common factors for the numerical part:

$300, 125$

Step 2

The factors for $300$ are $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300$ .

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Step 2.1

The factors for $300$ are all numbers between $1$ and $300$ , which divide $300$ evenly.

Check numbers between $1$ and $300$

Step 2.2

Find the factor pairs of $300$ where $x \cdot y = 300$ .

$\begin{array}{c} x & y \\ 1 & 300 \\ 2 & 150 \\ 3 & 100 \\ 4 & 75 \\ 5 & 60 \\ 6 & 50 \\ 10 & 30 \\ 12 & 25 \\ 15 & 20 \end{array}$

Step 2.3

List the factors for $300$ .

$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300$

Step 3

The factors for $125$ are $1, 5, 25, 125$ .

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Step 3.1

The factors for $125$ are all numbers between $1$ and $125$ , which divide $125$ evenly.

Check numbers between $1$ and $125$

Step 3.2

Find the factor pairs of $125$ where $x \cdot y = 125$ .

$\begin{array}{c} x & y \\ 1 & 125 \\ 5 & 25 \end{array}$

Step 3.3

List the factors for $125$ .

$1, 5, 25, 125$

Step 4

List all the factors for $300, 125$ to find the common factors.

$300$ : $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300$

$125$ : $1, 5, 25, 125$

Step 5

The common factors for $300, 125$ are $1, 5, 25$ .

$1, 5, 25$

Step 6

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

$25$