Step 1 :
Divide $ 2025 $ by $ 1089 $ and get the remainder

$$ 2025 : 1089 = 1 \text{ ( remainder is } \color{blue}{ 936 } \text{ ) } $$

The remainder is positive ($ 936 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1089 $ by $ \color{blue}{ 936 } $ and get the remainder

$$ 1089 : 936 = 1 \text{ ( remainder is } \color{blue}{ 153 } \text{ ) } $$

The remainder is still positive ($ 153 > 0 $), so we will continue with division.

Step 3 :
Divide $ 936 $ by $ \color{blue}{ 153 } $ and get the remainder

$$ 936 : 153 = 6 \text{ ( remainder is } \color{blue}{ 18 } \text{ ) } $$

The remainder is still positive ($ 18 > 0 $), so we will continue with division.

Step 4 :
Divide $ 153 $ by $ \color{blue}{ 18 } $ and get the remainder

$$ 153 : 18 = 8 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 5 :
Divide $ 18 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 18 : \color{blue}{ \boxed { 9 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 9 }} $.

This solution can be visualized using a Venn diagram.

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

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