def count_factors(n):
""" Counts the total number of divisors/factors of the provided number.
Here's the gist from http://mathforum.org/library/drmath/view/55843.html:
A number n can be represented as: n = x^a + y^b + z^c + ...
where x, y, z ... are the prime factors of n, and a, b, c, ... are their multiplicities.
The number of total divisors of n = (a+1) * (b+1) * (c+1) * ...
"""
# builds a dict-like Counter object, where the keys are the distinct prime factors, and the
# values are the multiplicity of that factor (aka, how many of that distinct factor were
# present in the prime factorization)
prime_factor_counter = Counter(prime_factors(n))
# get a list of the multiplicities of the prime factors + 1
prime_factor_multiplicities_plus_one = [(x + 1) for _, x in prime_factor_counter.most_common()]
# multiply those all together and return
multiply = lambda x, y: x * y
return reduce(multiply, prime_factor_multiplicities_plus_one, 1)
def test_example(self):
"""
Check the provided example.
"""
self.assertEqual([i for i in prime_factors(13195)], [5, 7, 13, 29])
def problem003(output, argument=600851475143):
"""
Solve Problem #3.
"""
output.put((3, max(prime_factors(argument))))
"""Problem 3: Largest prime factor.
Compute prime factors by continually dividing out smallest factor."""
import unittest
from utils.primes import prime_factors
if __name__ == "__main__":
print(max(prime_factors(600851475143)))
unittest.main()
#!/usr/bin/python from utils.primes import prime_factors print max(prime_factors(600851475143))
def problem_3():
print(max(prime_factors(600851475143)))
