Step 1 : Find prime factorization of each number.

$$\begin{aligned}654160 =& 2\cdot2\cdot2\cdot2\cdot5\cdot13\cdot17\cdot37\\[8pt]51480 =& 2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot11\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 654160 and 51480. )

Step 2 : Put a box around factors that are common for all numbers:

$$\begin{aligned}654160 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot2\cdot\color{Orange}{\boxed{5}}\cdot\color{Purple}{\boxed{13}}\cdot17\cdot37\\[8pt]51480 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot3\cdot3\cdot\color{Orange}{\boxed{5}}\cdot11\cdot\color{Purple}{\boxed{13}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot5\cdot13 = 520 $$

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

GCD Calculator