Step 1 :
Divide $ 15250 $ by $ 10250 $ and get the remainder

$$ 15250 : 10250 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10250 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10250 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 250 } \text{ ) } $$

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

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 250 } $ and get the remainder

$$ 5000 : \color{blue}{ \boxed { 250 }} = 20 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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