Number Theory

1+2+3...198+199+200 is 50*201 since you can pair up the first and last, 2nd and 2nd to last, etc. 

201 is 3*67 and 50 is 2*5^2. the greatest prime factor is $\boxed{ 67}$ :P

So, in order to calculate the list, we can use a handy trick. We simply take the largest number, multiply it by that number +1, and divide by 2. 

We have

$\frac{200 \cdot 201}{2}=20100$

The prime factorization of $20100$ is 

$20100 = 2^2 \cdot 3 \cdot 5^2 \cdot 67$

Thus, the greatest prime divisor is 67. 

Thanks! :)