Step 1 :
Divide $ 32768 $ by $ 272 $ and get the remainder

$$ 32768 : 272 = 120 \text{ ( remainder is } \color{blue}{ 128 } \text{ ) } $$

The remainder is positive ($ 128 > 0 $), so we will continue with division.

Step 2 :
Divide $ 272 $ by $ \color{blue}{ 128 } $ and get the remainder

$$ 272 : 128 = 2 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 3 :
Divide $ 128 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 128 : \color{blue}{ \boxed { 16 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 16 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator