Step 1 : Find prime factorization of each number.

$$\begin{aligned}682 =& 2\cdot11\cdot31\\[8pt]496 =& 2\cdot2\cdot2\cdot2\cdot31\\[8pt]\end{aligned}$$

(view steps on how to factor 682 and 496. )

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

$$\begin{aligned}682 =& \color{blue}{\boxed{2}}\cdot11\cdot\color{red}{\boxed{31}}\\[8pt]496 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot2\cdot\color{red}{\boxed{31}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot31 = 62 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator