Step 1 : Find prime factorization of each number.

$$\begin{aligned}30690 =& 2\cdot3\cdot3\cdot5\cdot11\cdot31\\[8pt]93093 =& 3\cdot7\cdot11\cdot13\cdot31\\[8pt]\end{aligned}$$

(view steps on how to factor 30690 and 93093. )

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

$$\begin{aligned}30690 =& 2\cdot\color{blue}{\boxed{3}}\cdot3\cdot5\cdot\color{red}{\boxed{11}}\cdot\color{Fuchsia}{\boxed{31}}\\[8pt]93093 =& \color{blue}{\boxed{3}}\cdot7\cdot\color{red}{\boxed{11}}\cdot13\cdot\color{Fuchsia}{\boxed{31}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot11\cdot31 = 1023 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator