Step 1 :
Divide $ 16650 $ by $ 11650 $ and get the remainder

$$ 16650 : 11650 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11650 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11650 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1650 } \text{ ) } $$

The remainder is still positive ($ 1650 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1650 } $ and get the remainder

$$ 5000 : 1650 = 3 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

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

Step 4 :
Divide $ 1650 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 1650 : \color{blue}{ \boxed { 50 }} = 33 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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