Step 1 :
Divide $ 18090 $ by $ 13090 $ and get the remainder

$$ 18090 : 13090 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13090 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13090 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3090 } \text{ ) } $$

The remainder is still positive ($ 3090 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3090 } $ and get the remainder

$$ 5000 : 3090 = 1 \text{ ( remainder is } \color{blue}{ 1910 } \text{ ) } $$

The remainder is still positive ($ 1910 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3090 $ by $ \color{blue}{ 1910 } $ and get the remainder

$$ 3090 : 1910 = 1 \text{ ( remainder is } \color{blue}{ 1180 } \text{ ) } $$

The remainder is still positive ($ 1180 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1910 $ by $ \color{blue}{ 1180 } $ and get the remainder

$$ 1910 : 1180 = 1 \text{ ( remainder is } \color{blue}{ 730 } \text{ ) } $$

The remainder is still positive ($ 730 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1180 $ by $ \color{blue}{ 730 } $ and get the remainder

$$ 1180 : 730 = 1 \text{ ( remainder is } \color{blue}{ 450 } \text{ ) } $$

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

Step 7 :
Divide $ 730 $ by $ \color{blue}{ 450 } $ and get the remainder

$$ 730 : 450 = 1 \text{ ( remainder is } \color{blue}{ 280 } \text{ ) } $$

The remainder is still positive ($ 280 > 0 $), so we will continue with division.

Step 8 :
Divide $ 450 $ by $ \color{blue}{ 280 } $ and get the remainder

$$ 450 : 280 = 1 \text{ ( remainder is } \color{blue}{ 170 } \text{ ) } $$

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

Step 9 :
Divide $ 280 $ by $ \color{blue}{ 170 } $ and get the remainder

$$ 280 : 170 = 1 \text{ ( remainder is } \color{blue}{ 110 } \text{ ) } $$

The remainder is still positive ($ 110 > 0 $), so we will continue with division.

Step 10 :
Divide $ 170 $ by $ \color{blue}{ 110 } $ and get the remainder

$$ 170 : 110 = 1 \text{ ( remainder is } \color{blue}{ 60 } \text{ ) } $$

The remainder is still positive ($ 60 > 0 $), so we will continue with division.

Step 11 :
Divide $ 110 $ by $ \color{blue}{ 60 } $ and get the remainder

$$ 110 : 60 = 1 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

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

Step 12 :
Divide $ 60 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 60 : 50 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 13 :
Divide $ 50 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 50 : \color{blue}{ \boxed { 10 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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