Step 1 :
Divide $ 16610 $ by $ 11610 $ and get the remainder

$$ 16610 : 11610 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11610 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11610 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1610 } \text{ ) } $$

The remainder is still positive ($ 1610 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1610 } $ and get the remainder

$$ 5000 : 1610 = 3 \text{ ( remainder is } \color{blue}{ 170 } \text{ ) } $$

The remainder is still positive ($ 170 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1610 $ by $ \color{blue}{ 170 } $ and get the remainder

$$ 1610 : 170 = 9 \text{ ( remainder is } \color{blue}{ 80 } \text{ ) } $$

The remainder is still positive ($ 80 > 0 $), so we will continue with division.

Step 5 :
Divide $ 170 $ by $ \color{blue}{ 80 } $ and get the remainder

$$ 170 : 80 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 6 :
Divide $ 80 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 80 : \color{blue}{ \boxed { 10 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.

This solution can be visualized using a Venn diagram.

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

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