Step 1 :
Divide $ 18010 $ by $ 13010 $ and get the remainder

$$ 18010 : 13010 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13010 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13010 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3010 } \text{ ) } $$

The remainder is still positive ($ 3010 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3010 } $ and get the remainder

$$ 5000 : 3010 = 1 \text{ ( remainder is } \color{blue}{ 1990 } \text{ ) } $$

The remainder is still positive ($ 1990 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3010 $ by $ \color{blue}{ 1990 } $ and get the remainder

$$ 3010 : 1990 = 1 \text{ ( remainder is } \color{blue}{ 1020 } \text{ ) } $$

The remainder is still positive ($ 1020 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1990 $ by $ \color{blue}{ 1020 } $ and get the remainder

$$ 1990 : 1020 = 1 \text{ ( remainder is } \color{blue}{ 970 } \text{ ) } $$

The remainder is still positive ($ 970 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1020 $ by $ \color{blue}{ 970 } $ and get the remainder

$$ 1020 : 970 = 1 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

The remainder is still positive ($ 50 > 0 $), so we will continue with division.

Step 7 :
Divide $ 970 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 970 : 50 = 19 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is still positive ($ 20 > 0 $), so we will continue with division.

Step 8 :
Divide $ 50 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 50 : 20 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 9 :
Divide $ 20 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 20 : \color{blue}{ \boxed { 10 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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