Step 1 :
Divide $ 171 $ by $ 129 $ and get the remainder

$$ 171 : 129 = 1 \text{ ( remainder is } \color{blue}{ 42 } \text{ ) } $$

The remainder is positive ($ 42 > 0 $), so we will continue with division.

Step 2 :
Divide $ 129 $ by $ \color{blue}{ 42 } $ and get the remainder

$$ 129 : 42 = 3 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 3 :
Divide $ 42 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 42 : \color{blue}{ \boxed { 3 }} = 14 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator