terrible_fizzbuzz

#O(n)
def crazy_modulo(n,mod):
    i = 0
    while(n>0):
        n-=1
        i+=1
        if(i==mod):
            i=0
    return i


# Random tidbit, according to a random reddit math lecture, supposedly, the average number of prime factors is ~O(log(n)), i shall use log(n)log(n) as the bound for all factors, which may be wrong, but i believe would err on the low side, as there is a set picking problem for combinations of prime factors to make non-prime factors but bounded not by the number of factors selected, but by the final product's size. I think a 2 factor selection would give you the squaring, and the actual bound would be some other odd exponent bounded by some function of N.
#O(n^2) +  (non-significant)  O(log(n)^2*log(log(n)))
def compute_all_factors(n):
    i = n
    factor_list = []
    while(i>0):
        if(crazy_modulo(n,i)==0):
            factor_list.append(i) # log(n)^2 times, cost(log(log(n)))
        i-=1
    return factor_list

# First pass + Filtering Pass
#O(n^2) + O((log(n)^2)*n^2)
def compute_prime_factors(n):
    factor_list = compute_all_factors(n)
    prime_factor_list = []
    for factor in factor_list:
        if(len(compute_all_factors(factor))==2): #O(n^2) +  (non-significant)  O(log(n)^2*log(log(n)))
            prime_factor_list.append(factor)
    return prime_factor_list

def fact_match(subset,superset):
    is_subset = True
    for i in subset:
        is_found = False
        for j in superset:
            if(i==j):
                is_found = True
        is_subset = is_subset and is_found
    return is_subset

# Overall most significant factor is O((log(n)^2)*n^3), though for small N, the lesser order terms are non-trivial by comparison.
# The lesser order terms are however quite hideous and i dont feel like trying to figure them all out.
def FizzBuzz(fizz,buzz,n):
    full_saying = ""
    i = 1
    fizzfact = compute_prime_factors(fizz)
    buzzfact = compute_prime_factors(buzz)
    while(i<=n):
        say = ""
        i_fact = compute_prime_factors(i)
        if(fact_match(fizzfact, i_fact)):
            say+="fizz"
        if(fact_match(buzzfact, i_fact)):
            say+="buzz"
        if(len(say)==0):
            say = "{}".format(i)
        full_saying += " "+say
        i+=1
    return full_saying


print(FizzBuzz(3,5,15))