Step 1 :
Divide $ 18050 $ by $ 13050 $ and get the remainder

$$ 18050 : 13050 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13050 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13050 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3050 } \text{ ) } $$

The remainder is still positive ($ 3050 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3050 } $ and get the remainder

$$ 5000 : 3050 = 1 \text{ ( remainder is } \color{blue}{ 1950 } \text{ ) } $$

The remainder is still positive ($ 1950 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3050 $ by $ \color{blue}{ 1950 } $ and get the remainder

$$ 3050 : 1950 = 1 \text{ ( remainder is } \color{blue}{ 1100 } \text{ ) } $$

The remainder is still positive ($ 1100 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1950 $ by $ \color{blue}{ 1100 } $ and get the remainder

$$ 1950 : 1100 = 1 \text{ ( remainder is } \color{blue}{ 850 } \text{ ) } $$

The remainder is still positive ($ 850 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1100 $ by $ \color{blue}{ 850 } $ and get the remainder

$$ 1100 : 850 = 1 \text{ ( remainder is } \color{blue}{ 250 } \text{ ) } $$

The remainder is still positive ($ 250 > 0 $), so we will continue with division.

Step 7 :
Divide $ 850 $ by $ \color{blue}{ 250 } $ and get the remainder

$$ 850 : 250 = 3 \text{ ( remainder is } \color{blue}{ 100 } \text{ ) } $$

The remainder is still positive ($ 100 > 0 $), so we will continue with division.

Step 8 :
Divide $ 250 $ by $ \color{blue}{ 100 } $ and get the remainder

$$ 250 : 100 = 2 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

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

Step 9 :
Divide $ 100 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 100 : \color{blue}{ \boxed { 50 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 50 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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