Find the GCF 54 , 81

$54$ , $81$

Step 1

Find the common factors for the numerical part:

$54, 81$

Step 2

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 3

The factors for $81$ are $1, 3, 9, 27, 81$ .

The factors for $81$ are all numbers between $1$ and $81$ , which divide $81$ evenly.

Check numbers between $1$ and $81$

Find the factor pairs of $81$ where $x \cdot y = 81$ .

$\begin{array}{c} x & y \\ 1 & 81 \\ 3 & 27 \\ 9 & 9 \end{array}$

List the factors for $81$ .

$1, 3, 9, 27, 81$

Step 4

List all the factors for $54, 81$ to find the common factors.

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

$81$ : $1, 3, 9, 27, 81$

Step 5

The common factors for $54, 81$ are $1, 3, 9, 27$ .

$1, 3, 9, 27$

Step 6

The GCF (HCF) of the numerical factors $1, 3, 9, 27$ is $27$ .

$27$