Step 1 :
Divide $ 20025 $ by $ 2025 $ and get the remainder

$$ 20025 : 2025 = 9 \text{ ( remainder is } \color{blue}{ 1800 } \text{ ) } $$

The remainder is positive ($ 1800 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2025 $ by $ \color{blue}{ 1800 } $ and get the remainder

$$ 2025 : 1800 = 1 \text{ ( remainder is } \color{blue}{ 225 } \text{ ) } $$

The remainder is still positive ($ 225 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1800 $ by $ \color{blue}{ 225 } $ and get the remainder

$$ 1800 : \color{blue}{ \boxed { 225 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 225 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator