Step 1 :
Divide $ 18110 $ by $ 13110 $ and get the remainder

$$ 18110 : 13110 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13110 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13110 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3110 } \text{ ) } $$

The remainder is still positive ($ 3110 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3110 } $ and get the remainder

$$ 5000 : 3110 = 1 \text{ ( remainder is } \color{blue}{ 1890 } \text{ ) } $$

The remainder is still positive ($ 1890 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3110 $ by $ \color{blue}{ 1890 } $ and get the remainder

$$ 3110 : 1890 = 1 \text{ ( remainder is } \color{blue}{ 1220 } \text{ ) } $$

The remainder is still positive ($ 1220 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1890 $ by $ \color{blue}{ 1220 } $ and get the remainder

$$ 1890 : 1220 = 1 \text{ ( remainder is } \color{blue}{ 670 } \text{ ) } $$

The remainder is still positive ($ 670 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1220 $ by $ \color{blue}{ 670 } $ and get the remainder

$$ 1220 : 670 = 1 \text{ ( remainder is } \color{blue}{ 550 } \text{ ) } $$

The remainder is still positive ($ 550 > 0 $), so we will continue with division.

Step 7 :
Divide $ 670 $ by $ \color{blue}{ 550 } $ and get the remainder

$$ 670 : 550 = 1 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

The remainder is still positive ($ 120 > 0 $), so we will continue with division.

Step 8 :
Divide $ 550 $ by $ \color{blue}{ 120 } $ and get the remainder

$$ 550 : 120 = 4 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

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

Step 9 :
Divide $ 120 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 120 : 70 = 1 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

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

Step 10 :
Divide $ 70 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 70 : 50 = 1 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

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

Step 11 :
Divide $ 50 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 50 : 20 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 12 :
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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