Just for the record – custom algorithm for searching greatest prime divisor of a number, O(n) worst-case (O(sqrt(n)) taken by prime detection):

def prime(num, get_number=False):
  for divisor in range(2, int(math.sqrt(num)) + 1):
    if num % divisor == 0:
      return False
  return num if get_number else True

def hydra_gpd(num, get_number=None):
  sequence = range(2, int(math.sqrt(num)) + 1)
  gpd = 1
  for divisor in sequence:
    divided = int(num / divisor)
    if num % divisor == 0:
      if prime(divisor) and divisor > gpd:
        gpd = divisor
      if prime(divided) and divided > gpd:
        gpd = divided
      recursive_gpd = hydra_gpd(divided)
      if recursive_gpd > gpd:
        gpd = recursive_gpd
      return gpd
  return gpd

Nothing too special, just to keep it around.