Step 1 :
Divide $ 16210 $ by $ 11210 $ and get the remainder

$$ 16210 : 11210 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11210 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11210 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1210 } \text{ ) } $$

The remainder is still positive ($ 1210 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1210 } $ and get the remainder

$$ 5000 : 1210 = 4 \text{ ( remainder is } \color{blue}{ 160 } \text{ ) } $$

The remainder is still positive ($ 160 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1210 $ by $ \color{blue}{ 160 } $ and get the remainder

$$ 1210 : 160 = 7 \text{ ( remainder is } \color{blue}{ 90 } \text{ ) } $$

The remainder is still positive ($ 90 > 0 $), so we will continue with division.

Step 5 :
Divide $ 160 $ by $ \color{blue}{ 90 } $ and get the remainder

$$ 160 : 90 = 1 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

The remainder is still positive ($ 70 > 0 $), so we will continue with division.

Step 6 :
Divide $ 90 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 90 : 70 = 1 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

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

Step 7 :
Divide $ 70 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 70 : 20 = 3 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 8 :
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