Step 1 :
Divide $ 12075 $ by $ 5655 $ and get the remainder

$$ 12075 : 5655 = 2 \text{ ( remainder is } \color{blue}{ 765 } \text{ ) } $$

The remainder is positive ($ 765 > 0 $), so we will continue with division.

Step 2 :
Divide $ 5655 $ by $ \color{blue}{ 765 } $ and get the remainder

$$ 5655 : 765 = 7 \text{ ( remainder is } \color{blue}{ 300 } \text{ ) } $$

The remainder is still positive ($ 300 > 0 $), so we will continue with division.

Step 3 :
Divide $ 765 $ by $ \color{blue}{ 300 } $ and get the remainder

$$ 765 : 300 = 2 \text{ ( remainder is } \color{blue}{ 165 } \text{ ) } $$

The remainder is still positive ($ 165 > 0 $), so we will continue with division.

Step 4 :
Divide $ 300 $ by $ \color{blue}{ 165 } $ and get the remainder

$$ 300 : 165 = 1 \text{ ( remainder is } \color{blue}{ 135 } \text{ ) } $$

The remainder is still positive ($ 135 > 0 $), so we will continue with division.

Step 5 :
Divide $ 165 $ by $ \color{blue}{ 135 } $ and get the remainder

$$ 165 : 135 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

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

Step 6 :
Divide $ 135 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 135 : 30 = 4 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

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

Step 7 :
Divide $ 30 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 30 : \color{blue}{ \boxed { 15 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

GCD Calculator