Step 1 :
Divide $ 16510 $ by $ 11510 $ and get the remainder

$$ 16510 : 11510 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11510 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11510 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1510 } \text{ ) } $$

The remainder is still positive ($ 1510 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1510 } $ and get the remainder

$$ 5000 : 1510 = 3 \text{ ( remainder is } \color{blue}{ 470 } \text{ ) } $$

The remainder is still positive ($ 470 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1510 $ by $ \color{blue}{ 470 } $ and get the remainder

$$ 1510 : 470 = 3 \text{ ( remainder is } \color{blue}{ 100 } \text{ ) } $$

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

Step 5 :
Divide $ 470 $ by $ \color{blue}{ 100 } $ and get the remainder

$$ 470 : 100 = 4 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

The remainder is still positive ($ 70 > 0 $), so we will continue with division.

Step 6 :
Divide $ 100 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 100 : 70 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 7 :
Divide $ 70 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 70 : 30 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 8 :
Divide $ 30 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 30 : \color{blue}{ \boxed { 10 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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