Step 1 :
Divide $ 17550 $ by $ 12550 $ and get the remainder

$$ 17550 : 12550 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 12550 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 12550 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 2550 } \text{ ) } $$

The remainder is still positive ($ 2550 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 2550 } $ and get the remainder

$$ 5000 : 2550 = 1 \text{ ( remainder is } \color{blue}{ 2450 } \text{ ) } $$

The remainder is still positive ($ 2450 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2550 $ by $ \color{blue}{ 2450 } $ and get the remainder

$$ 2550 : 2450 = 1 \text{ ( remainder is } \color{blue}{ 100 } \text{ ) } $$

The remainder is still positive ($ 100 > 0 $), so we will continue with division.

Step 5 :
Divide $ 2450 $ by $ \color{blue}{ 100 } $ and get the remainder

$$ 2450 : 100 = 24 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

The remainder is still positive ($ 50 > 0 $), so we will continue with division.

Step 6 :
Divide $ 100 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 100 : \color{blue}{ \boxed { 50 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 50 }} $.

This solution can be visualized using a Venn diagram.

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

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