#include <bits/stdc++.h>
using namespace std;
long long gcd(long long big, long long small) {
  if (big % small == 0) return small;
  return gcd(small, big % small);
}
int main() {
  int n;
  cin >> n;
  vector<long long> a(n);
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  sort(a.begin(), a.end());
  long long g = a[0];
  for (int i = 0; i < n; ++i) {
    g = gcd(a[i], g);
  }
  int ans = 0;
  for (long long i = 1; i * i <= g; ++i) {
    if (g % i == 0) {
      ++ans;
      if (i * i < g) ++ans;
    }
  }
  cout << ans << endl;
  return 0;
}
