The GCD of given numbers is 242.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}36542 =& 2\cdot11\cdot11\cdot151\\[8pt]22022 =& 2\cdot7\cdot11\cdot11\cdot13\\[8pt]\end{aligned}$$(view steps on how to factor 36542 and 22022. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}36542 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{11}}\cdot\color{Fuchsia}{\boxed{11}}\cdot151\\[8pt]22022 =& \color{blue}{\boxed{2}}\cdot7\cdot\color{red}{\boxed{11}}\cdot\color{Fuchsia}{\boxed{11}}\cdot13\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot11\cdot11 = 242 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.