Step 1 :
Divide $ 613 $ by $ 74 $ and get the remainder

$$ 613 : 74 = 8 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is positive ($ 21 > 0 $), so we will continue with division.

Step 2 :
Divide $ 74 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 74 : 21 = 3 \text{ ( remainder is } \color{blue}{ 11 } \text{ ) } $$

The remainder is still positive ($ 11 > 0 $), so we will continue with division.

Step 3 :
Divide $ 21 $ by $ \color{blue}{ 11 } $ and get the remainder

$$ 21 : 11 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 4 :
Divide $ 11 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 11 : 10 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 5 :
Divide $ 10 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 10 : \color{blue}{ \boxed { 1 }} = 10 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator