#include<iostream>
#include<algorithm> 
using namespace std;

const int  N = 1e5+10;
int a[N];
int res;

int gcd(int a,int b);

int main()
{

    int n;
    cin>>n;
    int i = 0;
    for(i = 0;i<n;i++)
        scanf("%d",&a[i]);
    sort(a,a+n);
    int d = a[1] - a[0];

    for(i = 1;i<n;i++)
    {
        d = gcd(d,a[i] - a[i-1]);
        if(d == 1 || d == 0)
            break;
    }
    if(d != 0)
        res = (a[n-1]-a[0])/d + 1;
    else
        res = n;
    cout<<res<<endl;
    return 0;
}

int gcd(int a,int b)
{
    if(b == 0)
        return a;
    return gcd(b,a%b);
}