公式就是：

$$\gcd(\lvert x_2 - x_1 \rvert, \lvert y_2 - y_1 \rvert) + 1$$

AC code：

#include <bits/stdc++.h>
using namespace std;
#define ll long long

int main() {
    ll x1, y1, x2, y2;
    while (cin >> x1 >> y1 >> x2 >> y2) {
        ll dx = abs(x2 - x1);
        ll dy = abs(y2 - y1);
        ll g = __gcd(dx, dy);
        if (dx == 0 && dy == 0) {
            cout << 0 << endl;
        } else {
            cout << g - 1 << endl;
        }
    }
    return 0;
}