Step 1 :
Divide $ 4056 $ by $ 674 $ and get the remainder

$$ 4056 : 674 = 6 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is positive ($ 12 > 0 $), so we will continue with division.

Step 2 :
Divide $ 674 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 674 : 12 = 56 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 3 :
Divide $ 12 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 12 : \color{blue}{ \boxed { 2 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator