Algorithm to find Largest prime factor of a number

Here’s the best algorithm I know of (in Python)

def prime_factors(n):
    """Returns all the prime factors of a positive integer"""
    factors = []
    d = 2
    while n > 1:
        while n % d == 0:
            factors.append(d)
            n /= d
        d = d + 1

    return factors


pfs = prime_factors(1000)
largest_prime_factor = max(pfs) # The largest element in the prime factor list

The above method runs in O(n) in the worst case (when the input is a prime number).

EDIT:
Below is the O(sqrt(n)) version, as suggested in the comment. Here is the code, once more.

def prime_factors(n):
    """Returns all the prime factors of a positive integer"""
    factors = []
    d = 2
    while n > 1:
        while n % d == 0:
            factors.append(d)
            n /= d
        d = d + 1
        if d*d > n:
            if n > 1: factors.append(n)
            break
    return factors


pfs = prime_factors(1000)
largest_prime_factor = max(pfs) # The largest element in the prime factor list