Step 1 :
Divide $ 17950 $ by $ 12950 $ and get the remainder

$$ 17950 : 12950 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 12950 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 12950 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 2950 } \text{ ) } $$

The remainder is still positive ($ 2950 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 2950 } $ and get the remainder

$$ 5000 : 2950 = 1 \text{ ( remainder is } \color{blue}{ 2050 } \text{ ) } $$

The remainder is still positive ($ 2050 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2950 $ by $ \color{blue}{ 2050 } $ and get the remainder

$$ 2950 : 2050 = 1 \text{ ( remainder is } \color{blue}{ 900 } \text{ ) } $$

The remainder is still positive ($ 900 > 0 $), so we will continue with division.

Step 5 :
Divide $ 2050 $ by $ \color{blue}{ 900 } $ and get the remainder

$$ 2050 : 900 = 2 \text{ ( remainder is } \color{blue}{ 250 } \text{ ) } $$

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

Step 6 :
Divide $ 900 $ by $ \color{blue}{ 250 } $ and get the remainder

$$ 900 : 250 = 3 \text{ ( remainder is } \color{blue}{ 150 } \text{ ) } $$

The remainder is still positive ($ 150 > 0 $), so we will continue with division.

Step 7 :
Divide $ 250 $ by $ \color{blue}{ 150 } $ and get the remainder

$$ 250 : 150 = 1 \text{ ( remainder is } \color{blue}{ 100 } \text{ ) } $$

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

Step 8 :
Divide $ 150 $ by $ \color{blue}{ 100 } $ and get the remainder

$$ 150 : 100 = 1 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

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

Step 9 :
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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