Step 1 :
Divide $ 18310 $ by $ 13310 $ and get the remainder

$$ 18310 : 13310 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13310 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13310 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3310 } \text{ ) } $$

The remainder is still positive ($ 3310 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3310 } $ and get the remainder

$$ 5000 : 3310 = 1 \text{ ( remainder is } \color{blue}{ 1690 } \text{ ) } $$

The remainder is still positive ($ 1690 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3310 $ by $ \color{blue}{ 1690 } $ and get the remainder

$$ 3310 : 1690 = 1 \text{ ( remainder is } \color{blue}{ 1620 } \text{ ) } $$

The remainder is still positive ($ 1620 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1690 $ by $ \color{blue}{ 1620 } $ and get the remainder

$$ 1690 : 1620 = 1 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

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

Step 6 :
Divide $ 1620 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 1620 : 70 = 23 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 7 :
Divide $ 70 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 70 : \color{blue}{ \boxed { 10 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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