Step 1 :
Divide $ 720 $ by $ 390 $ and get the remainder

$$ 720 : 390 = 1 \text{ ( remainder is } \color{blue}{ 330 } \text{ ) } $$

The remainder is positive ($ 330 > 0 $), so we will continue with division.

Step 2 :
Divide $ 390 $ by $ \color{blue}{ 330 } $ and get the remainder

$$ 390 : 330 = 1 \text{ ( remainder is } \color{blue}{ 60 } \text{ ) } $$

The remainder is still positive ($ 60 > 0 $), so we will continue with division.

Step 3 :
Divide $ 330 $ by $ \color{blue}{ 60 } $ and get the remainder

$$ 330 : 60 = 5 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 4 :
Divide $ 60 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 60 : \color{blue}{ \boxed { 30 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 30 }} $.

This solution can be visualized using a Venn diagram.

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

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