Step 1 : Find prime factorization of each number.

$$\begin{aligned}1008 =& 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot7\\[8pt]2520 =& 2\cdot2\cdot2\cdot3\cdot3\cdot5\cdot7\\[8pt]2016 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot7\\[8pt]\end{aligned}$$

(view steps on how to factor 1008, 2520 and 2016. )

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

$$\begin{aligned}1008 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot2\cdot\color{Orange}{\boxed{3}}\cdot\color{Purple}{\boxed{3}}\cdot\color{blue}{\boxed{7}}\\[8pt]2520 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{3}}\cdot\color{Purple}{\boxed{3}}\cdot5\cdot\color{blue}{\boxed{7}}\\[8pt]2016 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot2\cdot2\cdot\color{Orange}{\boxed{3}}\cdot\color{Purple}{\boxed{3}}\cdot\color{blue}{\boxed{7}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot3\cdot3\cdot7 = 504 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator