Step 1 :
Divide $ 16110 $ by $ 11110 $ and get the remainder

$$ 16110 : 11110 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11110 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11110 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1110 } \text{ ) } $$

The remainder is still positive ($ 1110 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1110 } $ and get the remainder

$$ 5000 : 1110 = 4 \text{ ( remainder is } \color{blue}{ 560 } \text{ ) } $$

The remainder is still positive ($ 560 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1110 $ by $ \color{blue}{ 560 } $ and get the remainder

$$ 1110 : 560 = 1 \text{ ( remainder is } \color{blue}{ 550 } \text{ ) } $$

The remainder is still positive ($ 550 > 0 $), so we will continue with division.

Step 5 :
Divide $ 560 $ by $ \color{blue}{ 550 } $ and get the remainder

$$ 560 : 550 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 6 :
Divide $ 550 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 550 : \color{blue}{ \boxed { 10 }} = 55 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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