Find the GCF 60 , 84

$60$ , $84$

Step 1

Find the common factors for the numerical part:

$60, 84$

Step 2

The factors for $60$ are $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$ .

The factors for $60$ are all numbers between $1$ and $60$ , which divide $60$ evenly.

Check numbers between $1$ and $60$

Find the factor pairs of $60$ where $x \cdot y = 60$ .

$\begin{array}{c} x & y \\ 1 & 60 \\ 2 & 30 \\ 3 & 20 \\ 4 & 15 \\ 5 & 12 \\ 6 & 10 \end{array}$

List the factors for $60$ .

$1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

Step 3

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 4

List all the factors for $60, 84$ to find the common factors.

$60$ : $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60$

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

Step 5

The common factors for $60, 84$ are $1, 2, 3, 4, 6, 12$ .

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

Step 6

The GCF (HCF) of the numerical factors $1, 2, 3, 4, 6, 12$ is $12$ .

$12$