Step 1 : Find prime factorization of each number.

$$\begin{aligned}40293 =& 3\cdot3\cdot11\cdot11\cdot37\\[8pt]50193 =& 3\cdot3\cdot3\cdot11\cdot13\cdot13\\[8pt]59829 =& 3\cdot7\cdot7\cdot11\cdot37\\[8pt]\end{aligned}$$

(view steps on how to factor 40293, 50193 and 59829. )

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

$$\begin{aligned}40293 =& \color{blue}{\boxed{3}}\cdot3\cdot\color{red}{\boxed{11}}\cdot11\cdot37\\[8pt]50193 =& \color{blue}{\boxed{3}}\cdot3\cdot3\cdot\color{red}{\boxed{11}}\cdot13\cdot13\\[8pt]59829 =& \color{blue}{\boxed{3}}\cdot7\cdot7\cdot\color{red}{\boxed{11}}\cdot37\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot11 = 33 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator