Step 1 :
Divide $ 15930 $ by $ 10930 $ and get the remainder

$$ 15930 : 10930 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10930 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10930 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 930 } \text{ ) } $$

The remainder is still positive ($ 930 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 930 } $ and get the remainder

$$ 5000 : 930 = 5 \text{ ( remainder is } \color{blue}{ 350 } \text{ ) } $$

The remainder is still positive ($ 350 > 0 $), so we will continue with division.

Step 4 :
Divide $ 930 $ by $ \color{blue}{ 350 } $ and get the remainder

$$ 930 : 350 = 2 \text{ ( remainder is } \color{blue}{ 230 } \text{ ) } $$

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

Step 5 :
Divide $ 350 $ by $ \color{blue}{ 230 } $ and get the remainder

$$ 350 : 230 = 1 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

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

Step 6 :
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 7 :
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 8 :
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.

GCD Calculator