Step 1 :
Divide $ 18290 $ by $ 13290 $ and get the remainder

$$ 18290 : 13290 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13290 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13290 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3290 } \text{ ) } $$

The remainder is still positive ($ 3290 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3290 } $ and get the remainder

$$ 5000 : 3290 = 1 \text{ ( remainder is } \color{blue}{ 1710 } \text{ ) } $$

The remainder is still positive ($ 1710 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3290 $ by $ \color{blue}{ 1710 } $ and get the remainder

$$ 3290 : 1710 = 1 \text{ ( remainder is } \color{blue}{ 1580 } \text{ ) } $$

The remainder is still positive ($ 1580 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1710 $ by $ \color{blue}{ 1580 } $ and get the remainder

$$ 1710 : 1580 = 1 \text{ ( remainder is } \color{blue}{ 130 } \text{ ) } $$

The remainder is still positive ($ 130 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1580 $ by $ \color{blue}{ 130 } $ and get the remainder

$$ 1580 : 130 = 12 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

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

Step 7 :
Divide $ 130 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 130 : 20 = 6 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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.

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