Step 1 :
Divide $ 682 $ by $ 496 $ and get the remainder

$$ 682 : 496 = 1 \text{ ( remainder is } \color{blue}{ 186 } \text{ ) } $$

The remainder is positive ($ 186 > 0 $), so we will continue with division.

Step 2 :
Divide $ 496 $ by $ \color{blue}{ 186 } $ and get the remainder

$$ 496 : 186 = 2 \text{ ( remainder is } \color{blue}{ 124 } \text{ ) } $$

The remainder is still positive ($ 124 > 0 $), so we will continue with division.

Step 3 :
Divide $ 186 $ by $ \color{blue}{ 124 } $ and get the remainder

$$ 186 : 124 = 1 \text{ ( remainder is } \color{blue}{ 62 } \text{ ) } $$

The remainder is still positive ($ 62 > 0 $), so we will continue with division.

Step 4 :
Divide $ 124 $ by $ \color{blue}{ 62 } $ and get the remainder

$$ 124 : \color{blue}{ \boxed { 62 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 62 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator