Step 1 :
Divide $ 2025 $ by $ 1109 $ and get the remainder

$$ 2025 : 1109 = 1 \text{ ( remainder is } \color{blue}{ 916 } \text{ ) } $$

The remainder is positive ($ 916 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1109 $ by $ \color{blue}{ 916 } $ and get the remainder

$$ 1109 : 916 = 1 \text{ ( remainder is } \color{blue}{ 193 } \text{ ) } $$

The remainder is still positive ($ 193 > 0 $), so we will continue with division.

Step 3 :
Divide $ 916 $ by $ \color{blue}{ 193 } $ and get the remainder

$$ 916 : 193 = 4 \text{ ( remainder is } \color{blue}{ 144 } \text{ ) } $$

The remainder is still positive ($ 144 > 0 $), so we will continue with division.

Step 4 :
Divide $ 193 $ by $ \color{blue}{ 144 } $ and get the remainder

$$ 193 : 144 = 1 \text{ ( remainder is } \color{blue}{ 49 } \text{ ) } $$

The remainder is still positive ($ 49 > 0 $), so we will continue with division.

Step 5 :
Divide $ 144 $ by $ \color{blue}{ 49 } $ and get the remainder

$$ 144 : 49 = 2 \text{ ( remainder is } \color{blue}{ 46 } \text{ ) } $$

The remainder is still positive ($ 46 > 0 $), so we will continue with division.

Step 6 :
Divide $ 49 $ by $ \color{blue}{ 46 } $ and get the remainder

$$ 49 : 46 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 7 :
Divide $ 46 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 46 : 3 = 15 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 8 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 3 : \color{blue}{ \boxed { 1 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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