Step 1 :
Divide $ 15650 $ by $ 10650 $ and get the remainder

$$ 15650 : 10650 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10650 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10650 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 650 } \text{ ) } $$

The remainder is still positive ($ 650 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 650 } $ and get the remainder

$$ 5000 : 650 = 7 \text{ ( remainder is } \color{blue}{ 450 } \text{ ) } $$

The remainder is still positive ($ 450 > 0 $), so we will continue with division.

Step 4 :
Divide $ 650 $ by $ \color{blue}{ 450 } $ and get the remainder

$$ 650 : 450 = 1 \text{ ( remainder is } \color{blue}{ 200 } \text{ ) } $$

The remainder is still positive ($ 200 > 0 $), so we will continue with division.

Step 5 :
Divide $ 450 $ by $ \color{blue}{ 200 } $ and get the remainder

$$ 450 : 200 = 2 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

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

Step 6 :
Divide $ 200 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 200 : \color{blue}{ \boxed { 50 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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