While reading Peter Shor's paper *Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer*, I came across the following quote:

"This scheme will thus work as long as $n$ is odd and not a prime power; finding factors of prime powers can be done efficiently with classical methods."

I have two questions:

(1) How does one efficiently determine if a given number $N$ is a prime power, and

(2) How does one efficiently determine the factorization of a prime power?

(Note: I have included these as separate questions since I am aware that many of the standard algorithms for determining a number is composite will not necessarily produce a proper factor.)