Step 1 :
Divide $ 15610 $ by $ 10610 $ and get the remainder

$$ 15610 : 10610 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10610 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10610 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 610 } \text{ ) } $$

The remainder is still positive ($ 610 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 610 } $ and get the remainder

$$ 5000 : 610 = 8 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

The remainder is still positive ($ 120 > 0 $), so we will continue with division.

Step 4 :
Divide $ 610 $ by $ \color{blue}{ 120 } $ and get the remainder

$$ 610 : 120 = 5 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 5 :
Divide $ 120 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 120 : \color{blue}{ \boxed { 10 }} = 12 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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