Find the GCF 81 , 21 , 14

$81$ , $21$ , $14$

Step 1

Find the common factors for the numerical part:

$81, 21, 14$

Step 2

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 3

The factors for $21$ are $1, 3, 7, 21$ .

The factors for $21$ are all numbers between $1$ and $21$ , which divide $21$ evenly.

Check numbers between $1$ and $21$

Find the factor pairs of $21$ where $x \cdot y = 21$ .

$\begin{array}{c} x & y \\ 1 & 21 \\ 3 & 7 \end{array}$

List the factors for $21$ .

$1, 3, 7, 21$

Step 4

The factors for $14$ are $1, 2, 7, 14$ .

The factors for $14$ are all numbers between $1$ and $14$ , which divide $14$ evenly.

Check numbers between $1$ and $14$

Find the factor pairs of $14$ where $x \cdot y = 14$ .

$\begin{array}{c} x & y \\ 1 & 14 \\ 2 & 7 \end{array}$

List the factors for $14$ .

$1, 2, 7, 14$

Step 5

List all the factors for $81, 21, 14$ to find the common factors.

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

$21$ : $1, 3, 7, 21$

$14$ : $1, 2, 7, 14$

Step 6

The common factors for $81, 21, 14$ are $1$ .

$1$

Step 7

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

$1$