Step 1 :
Divide $ 18250 $ by $ 13250 $ and get the remainder

$$ 18250 : 13250 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13250 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13250 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3250 } \text{ ) } $$

The remainder is still positive ($ 3250 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3250 } $ and get the remainder

$$ 5000 : 3250 = 1 \text{ ( remainder is } \color{blue}{ 1750 } \text{ ) } $$

The remainder is still positive ($ 1750 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3250 $ by $ \color{blue}{ 1750 } $ and get the remainder

$$ 3250 : 1750 = 1 \text{ ( remainder is } \color{blue}{ 1500 } \text{ ) } $$

The remainder is still positive ($ 1500 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1750 $ by $ \color{blue}{ 1500 } $ and get the remainder

$$ 1750 : 1500 = 1 \text{ ( remainder is } \color{blue}{ 250 } \text{ ) } $$

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

Step 6 :
Divide $ 1500 $ by $ \color{blue}{ 250 } $ and get the remainder

$$ 1500 : \color{blue}{ \boxed { 250 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 250 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator