Subset Product

import itertools
from itertools import combinations
from functools import reduce
from operator import mul
import math


# Subset Product: Find all divisors of TARGET, output the SIZE of ALL K-sets that have product
# equal to TARGET)

TARGET = math.factorial(12)
SET = [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
SET = set(SET)

divisors = []
for i in SET:
    if TARGET % i == 0:
        divisors.append(i)


divisors = sorted(divisors)

max_combo = []
for a in divisors:
    max_combo.append(a)
    if reduce(mul,max_combo) >= TARGET:
        if reduce(mul,max_combo) > TARGET:
            max_combo.pop()
            break
        else:
            break
count = 0
for A in range(len(max_combo), 0, -1):
    if A <= len(divisors):
        for X in combinations(divisors, A):
            count = count + 1
            if reduce(mul, X) == TARGET:
                print(X, 'K-Size: ',len(X))
                quit()
            if A == len(max_combo):
                break