Step 1 :
Divide $ 375 $ by $ 45 $ and get the remainder

$$ 375 : 45 = 8 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

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

Step 2 :
Divide $ 45 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 45 : \color{blue}{ \boxed { 15 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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