Step 1 :
Divide $ 513 $ by $ 81 $ and get the remainder

$$ 513 : 81 = 6 \text{ ( remainder is } \color{blue}{ 27 } \text{ ) } $$

The remainder is positive ($ 27 > 0 $), so we will continue with division.

Step 2 :
Divide $ 81 $ by $ \color{blue}{ 27 } $ and get the remainder

$$ 81 : \color{blue}{ \boxed { 27 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 27 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator