Step 1 :
Divide $ 518 $ by $ 94 $ and get the remainder

$$ 518 : 94 = 5 \text{ ( remainder is } \color{blue}{ 48 } \text{ ) } $$

The remainder is positive ($ 48 > 0 $), so we will continue with division.

Step 2 :
Divide $ 94 $ by $ \color{blue}{ 48 } $ and get the remainder

$$ 94 : 48 = 1 \text{ ( remainder is } \color{blue}{ 46 } \text{ ) } $$

The remainder is still positive ($ 46 > 0 $), so we will continue with division.

Step 3 :
Divide $ 48 $ by $ \color{blue}{ 46 } $ and get the remainder

$$ 48 : 46 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 4 :
Divide $ 46 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 46 : \color{blue}{ \boxed { 2 }} = 23 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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