In how many ways 1387 can written in the sum of $n,(n>2)$ Consecutive natural numbers In how many ways $1387$ can written in the sum of $n(n>2)$ Consecutive natural numbers?

1.$2$
2.$3$
3.$4$
4.$5$

First we can see that it can be written in the form of the sum of two Consecutive natural numbers.Try other cases.The answer is going to be $3$ but how can we prove it?If you find all three cases how can we be sure that there isn't any other?

If $1387$ is the sum of the $n$ natural numbers $a,a+1,a+2,\ldots, a+n-1$, then $$1387 = \frac{n\cdot(2a+n-1)}2 $$
and hence it suffices to compare all factorizations of $2774$ with the factorization $n\cdot (2a+n-1)$
