Step 1 :
Divide $ 15910 $ by $ 10910 $ and get the remainder

$$ 15910 : 10910 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10910 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10910 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 910 } \text{ ) } $$

The remainder is still positive ($ 910 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 910 } $ and get the remainder

$$ 5000 : 910 = 5 \text{ ( remainder is } \color{blue}{ 450 } \text{ ) } $$

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

Step 4 :
Divide $ 910 $ by $ \color{blue}{ 450 } $ and get the remainder

$$ 910 : 450 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 5 :
Divide $ 450 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 450 : \color{blue}{ \boxed { 10 }} = 45 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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