Step 1 :
Divide $ 16290 $ by $ 11290 $ and get the remainder

$$ 16290 : 11290 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11290 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11290 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1290 } \text{ ) } $$

The remainder is still positive ($ 1290 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1290 } $ and get the remainder

$$ 5000 : 1290 = 3 \text{ ( remainder is } \color{blue}{ 1130 } \text{ ) } $$

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

Step 4 :
Divide $ 1290 $ by $ \color{blue}{ 1130 } $ and get the remainder

$$ 1290 : 1130 = 1 \text{ ( remainder is } \color{blue}{ 160 } \text{ ) } $$

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

Step 5 :
Divide $ 1130 $ by $ \color{blue}{ 160 } $ and get the remainder

$$ 1130 : 160 = 7 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 6 :
Divide $ 160 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 160 : \color{blue}{ \boxed { 10 }} = 16 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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