Find the GCF 60 , 504

$60$ , $504$

Step 1

Find the common factors for the numerical part:

$60, 504$

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 $504$ are $1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504$ .

The factors for $504$ are all numbers between $1$ and $504$ , which divide $504$ evenly.

Check numbers between $1$ and $504$

Find the factor pairs of $504$ where $x \cdot y = 504$ .

$\begin{array}{c} x & y \\ 1 & 504 \\ 2 & 252 \\ 3 & 168 \\ 4 & 126 \\ 6 & 84 \\ 7 & 72 \\ 8 & 63 \\ 9 & 56 \\ 12 & 42 \\ 14 & 36 \\ 18 & 28 \\ 21 & 24 \end{array}$

List the factors for $504$ .

$1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504$

Step 4

List all the factors for $60, 504$ to find the common factors.

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

$504$ : $1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504$

Step 5

The common factors for $60, 504$ 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 $12$ .

$12$

Find the GCF 60 , 504

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