#include <bits/stdc++.h>
using namespace std;
bool cmp(long long int x, long long int y) { return x > y; }
long long int min(long long int a, long long int b) {
  if (a >= b)
    return b;
  else
    return a;
}
long long int max(long long int a, long long int b) {
  if (a >= b)
    return a;
  else
    return b;
}
long long int sumdig(long long int n) {
  long long int sum = 0;
  while (n > 0) {
    sum += (n % 10);
    n /= 10;
  }
  return sum;
}
long long int ndig(long long int n) {
  long long int l = 0;
  while (n > 0) {
    n /= 10;
    l++;
  }
  return l;
}
bool isprime(long long int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (long long int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
long long int gcd(long long int x, long long int y) {
  long long int a, b, t, gcd, lcm;
  a = x;
  b = y;
  while (b != 0) {
    t = b;
    b = a % b;
    a = t;
  }
  gcd = a;
  return gcd;
}
long long int cntdiv(long long int n) {
  long long int cnt = 0;
  for (long long int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        cnt++;
      else
        cnt = cnt + 2;
    }
  }
  return cnt;
}
void solve() {
  long long int n;
  cin >> n;
  long long int a[n];
  for (long long int i = 0; i < n; i++) cin >> a[i];
  long long int x = 0;
  for (long long int i = 0; i < n; i++) {
    x = gcd(x, a[i]);
  }
  cout << cntdiv(x) << '\n';
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int TEST = 1;
  while (TEST--) {
    solve();
  }
}
