new_contents: from math import gcd, sqrt, ceil
  
  n = int(input())
  a = list(map(int, input().split()))
  
  a = list(set(a))
  divisor = a[0]
  for ai in a[1:]:
      divisor = gcd(divisor, ai)
  
  result = 1      # 1 is always a divisor
  limit = ceil(sqrt(divisor)) + 1
  primes = [2] + list(range(3, limit, 2))
  for prime_factor in primes:
      power = 0
      while divisor % prime_factor == 0:
          divisor /= prime_factor
          power += 1
      if power > 0:
          result *= 1 + power
  
  print(result)
  
subject: Solve (1 accidental WA)