Step 1 :
Divide $ 225324 $ by $ 202851 $ and get the remainder

$$ 225324 : 202851 = 1 \text{ ( remainder is } \color{blue}{ 22473 } \text{ ) } $$

The remainder is positive ($ 22473 > 0 $), so we will continue with division.

Step 2 :
Divide $ 202851 $ by $ \color{blue}{ 22473 } $ and get the remainder

$$ 202851 : 22473 = 9 \text{ ( remainder is } \color{blue}{ 594 } \text{ ) } $$

The remainder is still positive ($ 594 > 0 $), so we will continue with division.

Step 3 :
Divide $ 22473 $ by $ \color{blue}{ 594 } $ and get the remainder

$$ 22473 : 594 = 37 \text{ ( remainder is } \color{blue}{ 495 } \text{ ) } $$

The remainder is still positive ($ 495 > 0 $), so we will continue with division.

Step 4 :
Divide $ 594 $ by $ \color{blue}{ 495 } $ and get the remainder

$$ 594 : 495 = 1 \text{ ( remainder is } \color{blue}{ 99 } \text{ ) } $$

The remainder is still positive ($ 99 > 0 $), so we will continue with division.

Step 5 :
Divide $ 495 $ by $ \color{blue}{ 99 } $ and get the remainder

$$ 495 : \color{blue}{ \boxed { 99 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 99 }} $.

This solution can be visualized using a Venn diagram.

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

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