Step 1 :
Divide $ 17750 $ by $ 12750 $ and get the remainder

$$ 17750 : 12750 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

The remainder is positive ($ 5000 > 0 $), so we will continue with division.

Step 2 :
Divide $ 12750 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 12750 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 2750 } \text{ ) } $$

The remainder is still positive ($ 2750 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 2750 } $ and get the remainder

$$ 5000 : 2750 = 1 \text{ ( remainder is } \color{blue}{ 2250 } \text{ ) } $$

The remainder is still positive ($ 2250 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2750 $ by $ \color{blue}{ 2250 } $ and get the remainder

$$ 2750 : 2250 = 1 \text{ ( remainder is } \color{blue}{ 500 } \text{ ) } $$

The remainder is still positive ($ 500 > 0 $), so we will continue with division.

Step 5 :
Divide $ 2250 $ by $ \color{blue}{ 500 } $ and get the remainder

$$ 2250 : 500 = 4 \text{ ( remainder is } \color{blue}{ 250 } \text{ ) } $$

The remainder is still positive ($ 250 > 0 $), so we will continue with division.

Step 6 :
Divide $ 500 $ by $ \color{blue}{ 250 } $ and get the remainder

$$ 500 : \color{blue}{ \boxed { 250 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 250 }} $.

This solution can be visualized using a Venn diagram.

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

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