#include <iostream>
#include <algorithm>
using namespace std;
const int N = 1E5 + 10;
int a[N];
int gcd(int n, int m){
    return m == 0 ? n : gcd(m, n % m);
}
int main(){
    int n;  cin >> n;
    for(int i = 0; i < n; i ++ )    cin >> a[i];
    sort(a, a + n);
    int res = a[1] - a[0];
    for(int i = 2; i < n; i ++ ){
        res = gcd(res, a[i] - a[i - 1]);
    }
    if(res == 0)    cout << n << endl;
    else    cout << (a[n - 1] - a[0]) / res + 1 << endl;
    return 0;
}