Step 1 : Find prime factorization of each number.

$$\begin{aligned}1176 =& 2\cdot2\cdot2\cdot3\cdot7\cdot7\\[8pt]504 =& 2\cdot2\cdot2\cdot3\cdot3\cdot7\\[8pt]\end{aligned}$$

(view steps on how to factor 1176 and 504. )

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

$$\begin{aligned}1176 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{3}}\cdot\color{Purple}{\boxed{7}}\cdot7\\[8pt]504 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{3}}\cdot3\cdot\color{Purple}{\boxed{7}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot3\cdot7 = 168 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator