Step 1 :
Divide $ 200025 $ by $ 20025 $ and get the remainder

$$ 200025 : 20025 = 9 \text{ ( remainder is } \color{blue}{ 19800 } \text{ ) } $$

The remainder is positive ($ 19800 > 0 $), so we will continue with division.

Step 2 :
Divide $ 20025 $ by $ \color{blue}{ 19800 } $ and get the remainder

$$ 20025 : 19800 = 1 \text{ ( remainder is } \color{blue}{ 225 } \text{ ) } $$

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

Step 3 :
Divide $ 19800 $ by $ \color{blue}{ 225 } $ and get the remainder

$$ 19800 : \color{blue}{ \boxed { 225 }} = 88 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

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