Find the GCF 39 , 54 , 30

$39$ , $54$ , $30$

Step 1

Find the common factors for the numerical part:

$39, 54, 30$

Step 2

The factors for $39$ are $1, 3, 13, 39$ .

The factors for $39$ are all numbers between $1$ and $39$ , which divide $39$ evenly.

Check numbers between $1$ and $39$

Find the factor pairs of $39$ where $x \cdot y = 39$ .

$\begin{array}{c} x & y \\ 1 & 39 \\ 3 & 13 \end{array}$

List the factors for $39$ .

$1, 3, 13, 39$

Step 3

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 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 $39, 54, 30$ to find the common factors.

$39$ : $1, 3, 13, 39$

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

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

Step 6

The common factors for $39, 54, 30$ are $1, 3$ .

$1, 3$

Step 7

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

$3$