Step 1 :
Divide $ 93093 $ by $ 30690 $ and get the remainder

$$ 93093 : 30690 = 3 \text{ ( remainder is } \color{blue}{ 1023 } \text{ ) } $$

The remainder is positive ($ 1023 > 0 $), so we will continue with division.

Step 2 :
Divide $ 30690 $ by $ \color{blue}{ 1023 } $ and get the remainder

$$ 30690 : \color{blue}{ \boxed { 1023 }} = 30 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1023 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator