What is the maximum possible value of $k$ 
What is the maximum possible value of $k$ for which $2013$ can be written as a sum of $k$ consecutive positive integers? 

I tried to write $2013$ as a sum of AP with common difference $1$ then factorize one side of the expression, I don't know if it's true or not, any help will be appraciated.

Suppose $a$ be the first integer in the $n$ consecutive integers. We get $$n(2a+n-1)=4026=2 \cdot  3\cdot  11\cdot  61$$
Now as $$2a+n-1>n \Rightarrow  4026> n^{2}$$
the maximum value of $n$ occurs at $n = 61.$
and we're done 
