Step 1 :
Divide $ 16130 $ by $ 11130 $ and get the remainder

$$ 16130 : 11130 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11130 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11130 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1130 } \text{ ) } $$

The remainder is still positive ($ 1130 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1130 } $ and get the remainder

$$ 5000 : 1130 = 4 \text{ ( remainder is } \color{blue}{ 480 } \text{ ) } $$

The remainder is still positive ($ 480 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1130 $ by $ \color{blue}{ 480 } $ and get the remainder

$$ 1130 : 480 = 2 \text{ ( remainder is } \color{blue}{ 170 } \text{ ) } $$

The remainder is still positive ($ 170 > 0 $), so we will continue with division.

Step 5 :
Divide $ 480 $ by $ \color{blue}{ 170 } $ and get the remainder

$$ 480 : 170 = 2 \text{ ( remainder is } \color{blue}{ 140 } \text{ ) } $$

The remainder is still positive ($ 140 > 0 $), so we will continue with division.

Step 6 :
Divide $ 170 $ by $ \color{blue}{ 140 } $ and get the remainder

$$ 170 : 140 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 7 :
Divide $ 140 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 140 : 30 = 4 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

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

Step 8 :
Divide $ 30 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 30 : 20 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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