Step 1 : Find prime factorization of each number.

$$\begin{aligned}37983 =& 3\cdot11\cdot1151\\[8pt]101640 =& 2\cdot2\cdot2\cdot3\cdot5\cdot7\cdot11\cdot11\\[8pt]\end{aligned}$$

(view steps on how to factor 37983 and 101640. )

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

$$\begin{aligned}37983 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{11}}\cdot1151\\[8pt]101640 =& 2\cdot2\cdot2\cdot\color{blue}{\boxed{3}}\cdot5\cdot7\cdot\color{red}{\boxed{11}}\cdot11\\[8pt]\end{aligned}$$

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