Step 1 : Find prime factorization of each number.

$$\begin{aligned}253704 =& 2\cdot2\cdot2\cdot3\cdot11\cdot31\cdot31\\[8pt]22909068 =& 2\cdot2\cdot3\cdot3\cdot3\cdot3\cdot3\cdot7\cdot7\cdot13\cdot37\\[8pt]\end{aligned}$$

(view steps on how to factor 253704 and 22909068. )

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

$$\begin{aligned}253704 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot\color{Fuchsia}{\boxed{3}}\cdot11\cdot31\cdot31\\[8pt]22909068 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{3}}\cdot3\cdot3\cdot3\cdot3\cdot7\cdot7\cdot13\cdot37\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot3 = 12 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator