output_description: Print the maximum number of divisors that can be chosen to satisfy the
  condition.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      A B
attempt: def mkou(A, B):
      x = A % B
      if x == 0:
          return B
      else:
          return mkou(B, x)
  
  
  def prime_F(k):
      a = [
          1,
      ]
      end = int(pow(k, 0.5))
      if k % 2 == 0:
          k /= 2
          a.append(2)
      k = int(k)
  
      for x in range(3, end, 1):
          if k % x == 0:
              while k % x == 0:
                  k /= x
              a.append(x)
              if k == 1:
                  break
      if k != 1:
          a.append(k)
      return a
  
  
  A, B = map(int, input().split())
  divA_array = []
  divB_array = []
  if A < B:
      A, B = B, A
  
  kouyaku = mkou(A, B)
  soinsu = prime_F(kouyaku)
  print(len(soinsu))
  
problem_description: Statement
  
  Given are positive integers A and B.
  
  Let us choose some number of positive common divisors of A and B.
  
  Here, any two of the chosen divisors must be coprime.
  
  At most, how many divisors can we choose?
  
  Definition of common divisor
  
  An integer d is said to be a common divisor of integers x and y when d divides
  both x and y.
  
  Definition of being coprime
  
  Integers x and y are said to be coprime when x and y have no positive common
  divisors other than 1.
  
  Definition of dividing
  
  An integer x is said to divide another integer y when there exists an integer
  \alpha such that y = \alpha x.
samples: [{"input": "12 18", "output": "3\n    \n\n12 and 18 have the following positive common divisors: 1, 2, 3, and 6.\n\n1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can\nchoose 1, 2, and 3, which achieve the maximum result.\n\n* * *"}, {"input": "420 660", "output": "4\n    \n\n* * *"}, {"input": "1 2019", "output": "1\n    \n\n1 and 2019 have no positive common divisors other than 1."}]