#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) { return a == 0 ? b : gcd(b % a, a); }
int getDivs(long long a) {
  long long res = 0;
  for (int(i) = (int)1; (i) <= (int)sqrt(a); ++(i)) {
    if (a % i == 0) {
      res += 2 - (a / i == i);
    }
  }
  return res;
}
int main() {
  int n;
  cin >> n;
  long long res = 0;
  for (int(i) = (int)1; (i) <= (int)n; ++(i)) {
    long long x;
    cin >> x;
    if (i == 1)
      res = x;
    else
      res = gcd(res, x);
  }
  res = getDivs(res);
  cout << res << endl;
}
