As an answer to my question, I think it does have all the factors n has. But I can't write mathematical proof of it, and so I can't make that statement. It's probably easy. I can write that in the opposite direction though:

let a, b, c, ..., z be the factors of N:

(a * b * c * ... * z) = N

then

(a * b * c * ... * z)² = N²

(pretty simple thinking)

but I can't write that in the other direction... I mean, begining with N² and it's factors, conclude that it has at least all the factors N has.