Prime Factorization

# factorization:- Time is O(log n).

class PrimeFactor:
    def __init__(self, n):
        self.primes = []
        self.n = n
        self.factorization()

    #Save all prime numbers between 1 to n.
    def seive(self):
        n = self.n
        look_up = set()

        for i in range(2, n+1):
            if i not in look_up:
                self.primes.append(i)
                for j in range(i*i, n+1, i):
                    look_up.add(j)

        return self.primes


    #Time is O(log n)
    def factorization(self):
        primes = self.seive()#assaign All prime numbers in primes.
        num = self.n
        s_root = int(num ** 0.5)#Square root value of given number.
        res = []

        for i in primes:
            if i > s_root:
                break
            while s_root <= num:
                if num % i == 0:
                    res.append(i)
                    num //= i #Floor division assignment.
                else:   #Break for next prime number.
                    break
        if num != 1:
            res.append(num)
        print("Output:", end=' ')
        print(' '.join(map(str, res)))


if __name__ == "__main__":
    while True:#Loop for test case.
        num = int(input())
        obj = PrimeFactor(num)