#include <bits/stdc++.h>
using namespace std;
const long long MAX = 1e6 + 1;
const long long PRIME = 1e9 + 7;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
vector<pair<long long, long long> > prime_factors(long long n) {
  vector<pair<long long, long long> > v;
  long long cnt = 0;
  while (n % 2 == 0) {
    cnt++;
    n /= 2;
  }
  if (cnt > 0) v.push_back(make_pair(2, cnt));
  for (long long i = 3; i <= sqrt(n); i += 2) {
    cnt = 0;
    while (n % i == 0) {
      cnt++;
      n /= i;
    }
    if (cnt > 0) v.push_back(make_pair(i, cnt));
  }
  if (n > 2) {
    v.push_back(make_pair(n, 1));
  }
  return v;
}
void solve() {
  long long n;
  cin >> n;
  long long a[n];
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
  }
  long long g = a[0];
  for (long long i = 0; i < n; i++) {
    g = gcd(a[i], g);
  }
  if (g == 1) {
    cout << 1;
    return;
  }
  vector<pair<long long, long long> > v = prime_factors(g);
  long long ans = 1;
  for (long long i = 0; i < v.size(); i++) {
    ans *= (v[i].second + 1);
  }
  cout << ans << "\n";
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t;
  t = 1;
  while (t--) {
    solve();
  }
}
