Prime factorization - list

Question

I am trying to implement a function primeFac() that takes as input a positive integer n and returns a list containing all the numbers in the prime factorization of n.

I have gotten this far but I think it would be better to use recursion here, not sure how to create a recursive code here, what would be the base case? to start with.

My code:

def primes(n):
    primfac = []
    d = 2
    while (n > 1):
         if n%d==0:
             primfac.append(d)
    # how do I continue from here... ?

Answer 1

A simple trial division:

def primes(n):
    primfac = []
    d = 2
    while d*d <= n:
        while (n % d) == 0:
            primfac.append(d)  # supposing you want multiple factors repeated
            n //= d
        d += 1
    if n > 1:
       primfac.append(n)
    return primfac

with O(sqrt(n)) complexity (worst case). You can easily improve it by special-casing 2 and looping only over odd d (or special-casing more small primes and looping over fewer possible divisors).