Step 1 : Find prime factorization of each number.

$$\begin{aligned}309692 =& 2\cdot2\cdot139\cdot557\\[8pt]556 =& 2\cdot2\cdot139\\[8pt]\end{aligned}$$

(view steps on how to factor 309692 and 556. )

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

$$\begin{aligned}309692 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{139}}\cdot557\\[8pt]556 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{139}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot139 = 556 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator