Step 1 :
Divide $ 2025 $ by $ 1286 $ and get the remainder

$$ 2025 : 1286 = 1 \text{ ( remainder is } \color{blue}{ 739 } \text{ ) } $$

The remainder is positive ($ 739 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1286 $ by $ \color{blue}{ 739 } $ and get the remainder

$$ 1286 : 739 = 1 \text{ ( remainder is } \color{blue}{ 547 } \text{ ) } $$

The remainder is still positive ($ 547 > 0 $), so we will continue with division.

Step 3 :
Divide $ 739 $ by $ \color{blue}{ 547 } $ and get the remainder

$$ 739 : 547 = 1 \text{ ( remainder is } \color{blue}{ 192 } \text{ ) } $$

The remainder is still positive ($ 192 > 0 $), so we will continue with division.

Step 4 :
Divide $ 547 $ by $ \color{blue}{ 192 } $ and get the remainder

$$ 547 : 192 = 2 \text{ ( remainder is } \color{blue}{ 163 } \text{ ) } $$

The remainder is still positive ($ 163 > 0 $), so we will continue with division.

Step 5 :
Divide $ 192 $ by $ \color{blue}{ 163 } $ and get the remainder

$$ 192 : 163 = 1 \text{ ( remainder is } \color{blue}{ 29 } \text{ ) } $$

The remainder is still positive ($ 29 > 0 $), so we will continue with division.

Step 6 :
Divide $ 163 $ by $ \color{blue}{ 29 } $ and get the remainder

$$ 163 : 29 = 5 \text{ ( remainder is } \color{blue}{ 18 } \text{ ) } $$

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

Step 7 :
Divide $ 29 $ by $ \color{blue}{ 18 } $ and get the remainder

$$ 29 : 18 = 1 \text{ ( remainder is } \color{blue}{ 11 } \text{ ) } $$

The remainder is still positive ($ 11 > 0 $), so we will continue with division.

Step 8 :
Divide $ 18 $ by $ \color{blue}{ 11 } $ and get the remainder

$$ 18 : 11 = 1 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 9 :
Divide $ 11 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 11 : 7 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 10 :
Divide $ 7 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 7 : 4 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 11 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 4 : 3 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 12 :
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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