# include <iostream>
# include <cmath>
# include <cstring>
# include <string>
# include <algorithm>
using namespace std;
int a[1000005];
int gcd (int a,int b){
	if (b==0) return a;
	return gcd (b,a%b); 
}  
int main (){
	ios::sync_with_stdio (false);
	cin.tie(NULL);
	cout.tie(NULL);
	int n;
	cin >>n;
	for (int i=1;i<=n;i++)
		cin >>a[i]; 
	sort (a+1,a+1+n);
	int gcdn=a[2]-a[1];
	for (int i=3;i<=n;i++)
		gcdn=gcd(gcdn,a[i]-a[i-1]);
	cout <<(a[n]-a[1])/gcdn+1<<endl;
	return 0;
}