Pre-Algebra Examples

$24$ , $10$ , $15$

Step 1

Find the common factors for the numerical part:

$24, 10, 15$

Step 2

The factors for $24$ are $1, 2, 3, 4, 6, 8, 12, 24$ .

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Step 2.1

The factors for $24$ are all numbers between $1$ and $24$ , which divide $24$ evenly.

Check numbers between $1$ and $24$

Step 2.2

Find the factor pairs of $24$ where $x \cdot y = 24$ .

$\begin{array}{c} x & y \\ 1 & 24 \\ 2 & 12 \\ 3 & 8 \\ 4 & 6 \end{array}$

Step 2.3

List the factors for $24$ .

$1, 2, 3, 4, 6, 8, 12, 24$

Step 3

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

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Step 3.1

The factors for $10$ are all numbers between $1$ and $10$ , which divide $10$ evenly.

Check numbers between $1$ and $10$

Step 3.2

Find the factor pairs of $10$ where $x \cdot y = 10$ .

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

Step 3.3

List the factors for $10$ .

$1, 2, 5, 10$

Step 4

The factors for $15$ are $1, 3, 5, 15$ .

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Step 4.1

The factors for $15$ are all numbers between $1$ and $15$ , which divide $15$ evenly.

Check numbers between $1$ and $15$

Step 4.2

Find the factor pairs of $15$ where $x \cdot y = 15$ .

$\begin{array}{c} x & y \\ 1 & 15 \\ 3 & 5 \end{array}$

Step 4.3

List the factors for $15$ .

$1, 3, 5, 15$

Step 5

List all the factors for $24, 10, 15$ to find the common factors.

$24$ : $1, 2, 3, 4, 6, 8, 12, 24$

$10$ : $1, 2, 5, 10$

$15$ : $1, 3, 5, 15$

Step 6

The common factors for $24, 10, 15$ are $1$ .

$1$

Step 7

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

$1$