Step 1 :
Divide $ 18030 $ by $ 13030 $ and get the remainder

$$ 18030 : 13030 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13030 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13030 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3030 } \text{ ) } $$

The remainder is still positive ($ 3030 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3030 } $ and get the remainder

$$ 5000 : 3030 = 1 \text{ ( remainder is } \color{blue}{ 1970 } \text{ ) } $$

The remainder is still positive ($ 1970 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3030 $ by $ \color{blue}{ 1970 } $ and get the remainder

$$ 3030 : 1970 = 1 \text{ ( remainder is } \color{blue}{ 1060 } \text{ ) } $$

The remainder is still positive ($ 1060 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1970 $ by $ \color{blue}{ 1060 } $ and get the remainder

$$ 1970 : 1060 = 1 \text{ ( remainder is } \color{blue}{ 910 } \text{ ) } $$

The remainder is still positive ($ 910 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1060 $ by $ \color{blue}{ 910 } $ and get the remainder

$$ 1060 : 910 = 1 \text{ ( remainder is } \color{blue}{ 150 } \text{ ) } $$

The remainder is still positive ($ 150 > 0 $), so we will continue with division.

Step 7 :
Divide $ 910 $ by $ \color{blue}{ 150 } $ and get the remainder

$$ 910 : 150 = 6 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 8 :
Divide $ 150 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 150 : \color{blue}{ \boxed { 10 }} = 15 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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