input: Write a python function to count the number of common divisors between two given numbers.
  assert countCommonDivisors(350, 400) == 5
  assert countCommonDivisors(12, 18) == 4
  assert countCommonDivisors(100, 200) == 9
output: def countCommonDivisors(a, b):
      def gcd(x, y):
          while y:
              x, y = y, x % y
          return x
  
      common_divisor_count = 0
      common_gcd = gcd(a, b)
      
      for i in range(1, common_gcd + 1):
          if common_gcd % i == 0:
              common_divisor_count += 1
      
      return common_divisor_count