Find the GCF 12 , 18 , 84

$12$ , $18$ , $84$

Step 1

Find the common factors for the numerical part:

$12, 18, 84$

Step 2

The factors for $12$ are $1, 2, 3, 4, 6, 12$ .

The factors for $12$ are all numbers between $1$ and $12$ , which divide $12$ evenly.

Check numbers between $1$ and $12$

Find the factor pairs of $12$ where $x \cdot y = 12$ .

$\begin{array}{c} x & y \\ 1 & 12 \\ 2 & 6 \\ 3 & 4 \end{array}$

List the factors for $12$ .

$1, 2, 3, 4, 6, 12$

Step 3

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

The factors for $18$ are all numbers between $1$ and $18$ , which divide $18$ evenly.

Check numbers between $1$ and $18$

Find the factor pairs of $18$ where $x \cdot y = 18$ .

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

List the factors for $18$ .

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

Step 4

The factors for $84$ are $1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$ .

The factors for $84$ are all numbers between $1$ and $84$ , which divide $84$ evenly.

Check numbers between $1$ and $84$

Find the factor pairs of $84$ where $x \cdot y = 84$ .

$\begin{array}{c} x & y \\ 1 & 84 \\ 2 & 42 \\ 3 & 28 \\ 4 & 21 \\ 6 & 14 \\ 7 & 12 \end{array}$

List the factors for $84$ .

$1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$

Step 5

List all the factors for $12, 18, 84$ to find the common factors.

$12$ : $1, 2, 3, 4, 6, 12$

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

$84$ : $1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$

Step 6

The common factors for $12, 18, 84$ are $1, 2, 3, 6$ .

$1, 2, 3, 6$

Step 7

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

$6$