Prime Factorization

#include <bits/stdc++.h>

using namespace std;

const int N = 1e6 + 7;

int pr[N];

vector <int> primeFactorization(int x) {
    vector <int> v;
    for (int i = 2; i <= x; i++) {
        while (x % i == 0) {
            v.push_back(i);
            x /= i;
        }
    }
    return v;
}
vector <int> primeFactorization2(int x) {
    vector <int> v;
    for (int i = 2; i * i <= x; i++) {
        while (x % i == 0) {
            v.push_back(i);
            x /= i;
        }
    }
    if (x > 1) {
        v.push_back(x);
    }
    return v;
}
vector <int> primeFactorization3(int x) {
    vector <int> v;
    while (x > 1) {
        int p = pr[x];
        v.push_back(p);
        x = x / p;
    }
    return v;
}

int main(){
    for (int i = 2; i < N; i++) {
        if (pr[i] == 0) {
            pr[i] = i;
            for (int j = i + i; j < N; j = j + i) {
                if (pr[j] == 0)
                    pr[j] = i;
            }
        }
    }

    int x;
    cin >> x;

    vector <int> v = primeFactorization3(x);

    for (int x : v) {
        cout << x << " ";
    }
}