Step 1 :
Divide $ 18330 $ by $ 13330 $ and get the remainder

$$ 18330 : 13330 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13330 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13330 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3330 } \text{ ) } $$

The remainder is still positive ($ 3330 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3330 } $ and get the remainder

$$ 5000 : 3330 = 1 \text{ ( remainder is } \color{blue}{ 1670 } \text{ ) } $$

The remainder is still positive ($ 1670 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3330 $ by $ \color{blue}{ 1670 } $ and get the remainder

$$ 3330 : 1670 = 1 \text{ ( remainder is } \color{blue}{ 1660 } \text{ ) } $$

The remainder is still positive ($ 1660 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1670 $ by $ \color{blue}{ 1660 } $ and get the remainder

$$ 1670 : 1660 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 6 :
Divide $ 1660 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 1660 : \color{blue}{ \boxed { 10 }} = 166 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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