Factoring a number $p^a q^b$ knowing its totient
Edit: The quoted question addresses only numbers of the form $p^a q^b$, I asked a general question for arbitrary $n$.
If $n$ is a prime or a product of 2 primes then knowing its totient $\varphi(n)$ allows us immediately to find the prime factorization of $n$.
How about a general case? Does knowing $\varphi(n)$
- give us a way how to find the prime factorization of $n$,
- help as find a prime factor of $n$, or at least
- help at in finding any factor of $n$? (This turns out to be obvious.)