



'''simple docstring'''





from __future__ import annotations




def lowerCAmelCase    (__A):



     """simple docstring"""



     _a           =    2
     _a           =    []
     while i * i <= n:
          if n % i:
               i += 1
          else:
               n //= i
               factors.append(__A)
     if n > 1:
          factors.append(__A)
     return factors


if __name__ == "__main__":
  import doctest

  doctest.testmod()








'''simple docstring'''





def lowerCAmelCase    (__A):



     """simple docstring"""



     if not isinstance(__A    ,      __A):
          raise ValueError('''multiplicative_persistence() only accepts integral values''')
     if num < 0:
          raise ValueError('''multiplicative_persistence() does not accept negative values''')

     _a           =    0
     _a           =    str(__A)

     while len(__A) != 1:
          _a           =    [int(__A) for i in num_string]

          _a           =    1
          for i in range(0    ,      len(__A)):
               total *= numbers[i]

          _a           =    str(__A)

          steps += 1
     return steps




def lowerCAmelCase    (__A):



     """simple docstring"""



     if not isinstance(__A    ,      __A):
          raise ValueError('''additive_persistence() only accepts integral values''')
     if num < 0:
          raise ValueError('''additive_persistence() does not accept negative values''')

     _a           =    0
     _a           =    str(__A)

     while len(__A) != 1:
          _a           =    [int(__A) for i in num_string]

          _a           =    0
          for i in range(0    ,      len(__A)):
               total += numbers[i]

          _a           =    str(__A)

          steps += 1
     return steps


if __name__ == "__main__":
  import doctest

  doctest.testmod()



