#include <bits/stdc++.h>

#define ll long long

using namespace std;

ll nod(ll n) {
    vector<ll>v;
    if (n==1) return 1;
    for (int i=2; i*i<=n; i++) {
        if (n%i==0) v.push_back(0);
        while (n%i==0) {
            n/=i;
            v.back()++;
        }
        if (n==1) break;
    }
    if (n!=1) v.push_back(1);
    ll ans=1;
    for (auto i:v) ans*=(i+1);
    return ans;
}

int main() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    ll n;
    cin >> n;
    ll x=0;
    for (int i=0; i<n; i++) {
        ll v;
        cin >> v;
        x=gcd(v,x);
    }
    cout << nod(x);
    return 0;
}

/*
 */