Step 1 :
Divide $ 18150 $ by $ 13150 $ and get the remainder

$$ 18150 : 13150 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13150 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13150 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3150 } \text{ ) } $$

The remainder is still positive ($ 3150 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3150 } $ and get the remainder

$$ 5000 : 3150 = 1 \text{ ( remainder is } \color{blue}{ 1850 } \text{ ) } $$

The remainder is still positive ($ 1850 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3150 $ by $ \color{blue}{ 1850 } $ and get the remainder

$$ 3150 : 1850 = 1 \text{ ( remainder is } \color{blue}{ 1300 } \text{ ) } $$

The remainder is still positive ($ 1300 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1850 $ by $ \color{blue}{ 1300 } $ and get the remainder

$$ 1850 : 1300 = 1 \text{ ( remainder is } \color{blue}{ 550 } \text{ ) } $$

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

Step 6 :
Divide $ 1300 $ by $ \color{blue}{ 550 } $ and get the remainder

$$ 1300 : 550 = 2 \text{ ( remainder is } \color{blue}{ 200 } \text{ ) } $$

The remainder is still positive ($ 200 > 0 $), so we will continue with division.

Step 7 :
Divide $ 550 $ by $ \color{blue}{ 200 } $ and get the remainder

$$ 550 : 200 = 2 \text{ ( remainder is } \color{blue}{ 150 } \text{ ) } $$

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

Step 8 :
Divide $ 200 $ by $ \color{blue}{ 150 } $ and get the remainder

$$ 200 : 150 = 1 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

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

Step 9 :
Divide $ 150 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 150 : \color{blue}{ \boxed { 50 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

GCD Calculator