Step 1 :
Divide $ 15510 $ by $ 10510 $ and get the remainder

$$ 15510 : 10510 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10510 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10510 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 510 } \text{ ) } $$

The remainder is still positive ($ 510 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 510 } $ and get the remainder

$$ 5000 : 510 = 9 \text{ ( remainder is } \color{blue}{ 410 } \text{ ) } $$

The remainder is still positive ($ 410 > 0 $), so we will continue with division.

Step 4 :
Divide $ 510 $ by $ \color{blue}{ 410 } $ and get the remainder

$$ 510 : 410 = 1 \text{ ( remainder is } \color{blue}{ 100 } \text{ ) } $$

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

Step 5 :
Divide $ 410 $ by $ \color{blue}{ 100 } $ and get the remainder

$$ 410 : 100 = 4 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 6 :
Divide $ 100 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 100 : \color{blue}{ \boxed { 10 }} = 10 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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