Step 1 :
Divide $ 1080 $ by $ 615 $ and get the remainder

$$ 1080 : 615 = 1 \text{ ( remainder is } \color{blue}{ 465 } \text{ ) } $$

The remainder is positive ($ 465 > 0 $), so we will continue with division.

Step 2 :
Divide $ 615 $ by $ \color{blue}{ 465 } $ and get the remainder

$$ 615 : 465 = 1 \text{ ( remainder is } \color{blue}{ 150 } \text{ ) } $$

The remainder is still positive ($ 150 > 0 $), so we will continue with division.

Step 3 :
Divide $ 465 $ by $ \color{blue}{ 150 } $ and get the remainder

$$ 465 : 150 = 3 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

The remainder is still positive ($ 15 > 0 $), so we will continue with division.

Step 4 :
Divide $ 150 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 150 : \color{blue}{ \boxed { 15 }} = 10 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 15 }} $.

This solution can be visualized using a Venn diagram.

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

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