Step 1 :
Divide $ 621 $ by $ 333 $ and get the remainder

$$ 621 : 333 = 1 \text{ ( remainder is } \color{blue}{ 288 } \text{ ) } $$

The remainder is positive ($ 288 > 0 $), so we will continue with division.

Step 2 :
Divide $ 333 $ by $ \color{blue}{ 288 } $ and get the remainder

$$ 333 : 288 = 1 \text{ ( remainder is } \color{blue}{ 45 } \text{ ) } $$

The remainder is still positive ($ 45 > 0 $), so we will continue with division.

Step 3 :
Divide $ 288 $ by $ \color{blue}{ 45 } $ and get the remainder

$$ 288 : 45 = 6 \text{ ( remainder is } \color{blue}{ 18 } \text{ ) } $$

The remainder is still positive ($ 18 > 0 $), so we will continue with division.

Step 4 :
Divide $ 45 $ by $ \color{blue}{ 18 } $ and get the remainder

$$ 45 : 18 = 2 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 5 :
Divide $ 18 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 18 : \color{blue}{ \boxed { 9 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 9 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator