Prime Factorization

prime_factorization.py

p = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}
n = 7775460
l = []
n1 = 0

while n not in p:
    if n % 2 == 0:
        n = n // 2
        l.append(2)
    else:
        for num in [3, 5, 7, 11, 13, 17]:
            if n % num == 0:
                n = n // num
                n1 = n
                l.append(num)
                break
            else:
                pass
    if n in p:
        l.append(n1)
    else:
        pass

s = ''
for n in sorted(list(set(l))):
    if l.count(n) > 1:
        s += f'({n}**{l.count(n)})'
    else:
        s += f'({n})'

print(s)

prime_factorization_notes.txt

  7775460 should return '(2**2)(3**3)(5)(7)(11**2)(17)'
 /       \
2         3887730
         /       \
        2         1943865
                 /       \
                3         647955
                         /      \
                        3        215985
                                /      \
                               3        71995
                                       /     \
                                      5       14399
                                             /     \
                                            7       2057
                                                   /    \
                                                 11      187
                                                        /   \
                                                      11     17
===============================================================
  86240 should return '(2**5)(5)(7**2)(11)'
 /     \
2       43120
       /     \
      2       21560
             /     \
            2       10780
                   /     \
                  2       5390
                         /    \
                        2      2695
                              /    \
                             5      539
                                   /   \
                                  7     77
                                       /  \
                                      7    11
=============================================
  100 should return '(2**2)(5**5)'
 /   \
2     50
     /  \
    2    25
        /  \
       5    5