Step 1 :
Divide $ 18130 $ by $ 13130 $ and get the remainder

$$ 18130 : 13130 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13130 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13130 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3130 } \text{ ) } $$

The remainder is still positive ($ 3130 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3130 } $ and get the remainder

$$ 5000 : 3130 = 1 \text{ ( remainder is } \color{blue}{ 1870 } \text{ ) } $$

The remainder is still positive ($ 1870 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3130 $ by $ \color{blue}{ 1870 } $ and get the remainder

$$ 3130 : 1870 = 1 \text{ ( remainder is } \color{blue}{ 1260 } \text{ ) } $$

The remainder is still positive ($ 1260 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1870 $ by $ \color{blue}{ 1260 } $ and get the remainder

$$ 1870 : 1260 = 1 \text{ ( remainder is } \color{blue}{ 610 } \text{ ) } $$

The remainder is still positive ($ 610 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1260 $ by $ \color{blue}{ 610 } $ and get the remainder

$$ 1260 : 610 = 2 \text{ ( remainder is } \color{blue}{ 40 } \text{ ) } $$

The remainder is still positive ($ 40 > 0 $), so we will continue with division.

Step 7 :
Divide $ 610 $ by $ \color{blue}{ 40 } $ and get the remainder

$$ 610 : 40 = 15 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 8 :
Divide $ 40 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 40 : \color{blue}{ \boxed { 10 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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