Step 1 :
Divide $ 15310 $ by $ 10130 $ and get the remainder

$$ 15310 : 10130 = 1 \text{ ( remainder is } \color{blue}{ 5180 } \text{ ) } $$

The remainder is positive ($ 5180 > 0 $), so we will continue with division.

Step 2 :
Divide $ 10130 $ by $ \color{blue}{ 5180 } $ and get the remainder

$$ 10130 : 5180 = 1 \text{ ( remainder is } \color{blue}{ 4950 } \text{ ) } $$

The remainder is still positive ($ 4950 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5180 $ by $ \color{blue}{ 4950 } $ and get the remainder

$$ 5180 : 4950 = 1 \text{ ( remainder is } \color{blue}{ 230 } \text{ ) } $$

The remainder is still positive ($ 230 > 0 $), so we will continue with division.

Step 4 :
Divide $ 4950 $ by $ \color{blue}{ 230 } $ and get the remainder

$$ 4950 : 230 = 21 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

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

Step 5 :
Divide $ 230 $ by $ \color{blue}{ 120 } $ and get the remainder

$$ 230 : 120 = 1 \text{ ( remainder is } \color{blue}{ 110 } \text{ ) } $$

The remainder is still positive ($ 110 > 0 $), so we will continue with division.

Step 6 :
Divide $ 120 $ by $ \color{blue}{ 110 } $ and get the remainder

$$ 120 : 110 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 7 :
Divide $ 110 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 110 : \color{blue}{ \boxed { 10 }} = 11 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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