Step 1 :
Divide $ 17850 $ by $ 12850 $ and get the remainder

$$ 17850 : 12850 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 12850 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 12850 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 2850 } \text{ ) } $$

The remainder is still positive ($ 2850 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 2850 } $ and get the remainder

$$ 5000 : 2850 = 1 \text{ ( remainder is } \color{blue}{ 2150 } \text{ ) } $$

The remainder is still positive ($ 2150 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2850 $ by $ \color{blue}{ 2150 } $ and get the remainder

$$ 2850 : 2150 = 1 \text{ ( remainder is } \color{blue}{ 700 } \text{ ) } $$

The remainder is still positive ($ 700 > 0 $), so we will continue with division.

Step 5 :
Divide $ 2150 $ by $ \color{blue}{ 700 } $ and get the remainder

$$ 2150 : 700 = 3 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

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

Step 6 :
Divide $ 700 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 700 : \color{blue}{ \boxed { 50 }} = 14 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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