Find the GCF 60 , 14 , 21

$60$ , $14$ , $21$

Step 1

Find the common factors for the numerical part:

$60, 14, 21$

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 $14$ 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 4

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 5

List all the factors for $60, 14, 21$ to find the common factors.

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

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

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

Step 6

The common factors for $60, 14, 21$ are $1$ .

$1$

Step 7

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

$1$