Step 1 :
Divide $ 16090 $ by $ 11090 $ and get the remainder

$$ 16090 : 11090 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11090 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11090 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1090 } \text{ ) } $$

The remainder is still positive ($ 1090 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1090 } $ and get the remainder

$$ 5000 : 1090 = 4 \text{ ( remainder is } \color{blue}{ 640 } \text{ ) } $$

The remainder is still positive ($ 640 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1090 $ by $ \color{blue}{ 640 } $ and get the remainder

$$ 1090 : 640 = 1 \text{ ( remainder is } \color{blue}{ 450 } \text{ ) } $$

The remainder is still positive ($ 450 > 0 $), so we will continue with division.

Step 5 :
Divide $ 640 $ by $ \color{blue}{ 450 } $ and get the remainder

$$ 640 : 450 = 1 \text{ ( remainder is } \color{blue}{ 190 } \text{ ) } $$

The remainder is still positive ($ 190 > 0 $), so we will continue with division.

Step 6 :
Divide $ 450 $ by $ \color{blue}{ 190 } $ and get the remainder

$$ 450 : 190 = 2 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

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

Step 7 :
Divide $ 190 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 190 : 70 = 2 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

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

Step 8 :
Divide $ 70 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 70 : 50 = 1 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

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

Step 9 :
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 10 :
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.

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