#include <bits/stdc++.h>
using namespace std;
long long cmmdc(long long a, long long b) {
  long long r = a % b;
  do {
    r = a % b;
    a = b;
    b = r;
  } while (b);
  return a;
}
int main() {
  long long n, c, gcd;
  cin >> n;
  cin >> c;
  gcd = c;
  for (long long i = 2; i <= n; i++) {
    cin >> c;
    gcd = cmmdc(c, gcd);
  }
  long long lim = (long long)sqrt(double(gcd)), nr = 0;
  for (long long i = 1; i <= lim; i++) {
    if (gcd % i == 0) nr += 2;
  }
  if (lim * lim == gcd) nr--;
  cout << nr;
  return 0;
}
