Find the GCF 105 , 165 , 30

$105$ , $165$ , $30$

Step 1

Find the common factors for the numerical part:

$105, 165, 30$

Step 2

The factors for $105$ are $1, 3, 5, 7, 15, 21, 35, 105$ .

The factors for $105$ are all numbers between $1$ and $105$ , which divide $105$ evenly.

Check numbers between $1$ and $105$

Find the factor pairs of $105$ where $x \cdot y = 105$ .

$\begin{array}{c} x & y \\ 1 & 105 \\ 3 & 35 \\ 5 & 21 \\ 7 & 15 \end{array}$

List the factors for $105$ .

$1, 3, 5, 7, 15, 21, 35, 105$

Step 3

The factors for $165$ are $1, 3, 5, 11, 15, 33, 55, 165$ .

The factors for $165$ are all numbers between $1$ and $165$ , which divide $165$ evenly.

Check numbers between $1$ and $165$

Find the factor pairs of $165$ where $x \cdot y = 165$ .

$\begin{array}{c} x & y \\ 1 & 165 \\ 3 & 55 \\ 5 & 33 \\ 11 & 15 \end{array}$

List the factors for $165$ .

$1, 3, 5, 11, 15, 33, 55, 165$

Step 4

The factors for $30$ are $1, 2, 3, 5, 6, 10, 15, 30$ .

The factors for $30$ are all numbers between $1$ and $30$ , which divide $30$ evenly.

Check numbers between $1$ and $30$

Find the factor pairs of $30$ where $x \cdot y = 30$ .

$\begin{array}{c} x & y \\ 1 & 30 \\ 2 & 15 \\ 3 & 10 \\ 5 & 6 \end{array}$

List the factors for $30$ .

$1, 2, 3, 5, 6, 10, 15, 30$

Step 5

List all the factors for $105, 165, 30$ to find the common factors.

$105$ : $1, 3, 5, 7, 15, 21, 35, 105$

$165$ : $1, 3, 5, 11, 15, 33, 55, 165$

$30$ : $1, 2, 3, 5, 6, 10, 15, 30$

Step 6

The common factors for $105, 165, 30$ are $1, 3, 5, 15$ .

$1, 3, 5, 15$

Step 7

The GCF (HCF) of the numerical factors $1, 3, 5, 15$ is $15$ .

$15$