Step 1 :
Divide $ 18190 $ by $ 13190 $ and get the remainder

$$ 18190 : 13190 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13190 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13190 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3190 } \text{ ) } $$

The remainder is still positive ($ 3190 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3190 } $ and get the remainder

$$ 5000 : 3190 = 1 \text{ ( remainder is } \color{blue}{ 1810 } \text{ ) } $$

The remainder is still positive ($ 1810 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3190 $ by $ \color{blue}{ 1810 } $ and get the remainder

$$ 3190 : 1810 = 1 \text{ ( remainder is } \color{blue}{ 1380 } \text{ ) } $$

The remainder is still positive ($ 1380 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1810 $ by $ \color{blue}{ 1380 } $ and get the remainder

$$ 1810 : 1380 = 1 \text{ ( remainder is } \color{blue}{ 430 } \text{ ) } $$

The remainder is still positive ($ 430 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1380 $ by $ \color{blue}{ 430 } $ and get the remainder

$$ 1380 : 430 = 3 \text{ ( remainder is } \color{blue}{ 90 } \text{ ) } $$

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

Step 7 :
Divide $ 430 $ by $ \color{blue}{ 90 } $ and get the remainder

$$ 430 : 90 = 4 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

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

Step 8 :
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 9 :
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 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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