Find the GCF 30 , 42 , 54

$30$ , $42$ , $54$

Step 1

Find the common factors for the numerical part:

$30, 42, 54$

Step 2

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 3

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 4

The factors for $54$ are $1, 2, 3, 6, 9, 18, 27, 54$ .

The factors for $54$ are all numbers between $1$ and $54$ , which divide $54$ evenly.

Check numbers between $1$ and $54$

Find the factor pairs of $54$ where $x \cdot y = 54$ .

$\begin{array}{c} x & y \\ 1 & 54 \\ 2 & 27 \\ 3 & 18 \\ 6 & 9 \end{array}$

List the factors for $54$ .

$1, 2, 3, 6, 9, 18, 27, 54$

Step 5

List all the factors for $30, 42, 54$ to find the common factors.

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

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

$54$ : $1, 2, 3, 6, 9, 18, 27, 54$

Step 6

The common factors for $30, 42, 54$ are $1, 2, 3, 6$ .

$1, 2, 3, 6$

Step 7

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

$6$