Find the GCF 42 , 30 , 90

$42$ , $30$ , $90$

Step 1

Find the common factors for the numerical part:

$42, 30, 90$

Step 2

The factors for $42$ are $1, 2, 3, 6, 7, 14, 21, 42$ .

The factors for $42$ are all numbers between $1$ and $42$ , which divide $42$ evenly.

Check numbers between $1$ and $42$

Find the factor pairs of $42$ where $x \cdot y = 42$ .

$\begin{array}{c} x & y \\ 1 & 42 \\ 2 & 21 \\ 3 & 14 \\ 6 & 7 \end{array}$

List the factors for $42$ .

$1, 2, 3, 6, 7, 14, 21, 42$

Step 3

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 4

The factors for $90$ are $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$ .

The factors for $90$ are all numbers between $1$ and $90$ , which divide $90$ evenly.

Check numbers between $1$ and $90$

Find the factor pairs of $90$ where $x \cdot y = 90$ .

$\begin{array}{c} x & y \\ 1 & 90 \\ 2 & 45 \\ 3 & 30 \\ 5 & 18 \\ 6 & 15 \\ 9 & 10 \end{array}$

List the factors for $90$ .

$1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

Step 5

List all the factors for $42, 30, 90$ to find the common factors.

$42$ : $1, 2, 3, 6, 7, 14, 21, 42$

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

$90$ : $1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

Step 6

The common factors for $42, 30, 90$ are $1, 2, 3, 6$ .

$1, 2, 3, 6$

Step 7

The GCF (HCF) of the numerical factors $1, 2, 3, 6$ is $6$ .

$6$