Step 1 :
Divide $ 462 $ by $ 58 $ and get the remainder

$$ 462 : 58 = 7 \text{ ( remainder is } \color{blue}{ 56 } \text{ ) } $$

The remainder is positive ($ 56 > 0 $), so we will continue with division.

Step 2 :
Divide $ 58 $ by $ \color{blue}{ 56 } $ and get the remainder

$$ 58 : 56 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 3 :
Divide $ 56 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 56 : \color{blue}{ \boxed { 2 }} = 28 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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