Sieve Prime & Prime Factorization

/*
 1. Finding primes with sieve method
 2. Prime factorization
 * */
#include <bits/stdc++.h>
using namespace std;

#define N 1000005

bool num[N];
int primes[N];
int total = 0;
int divisors[500];
int ndiv;

void sieve()
{
    int i, j, k;

    memset(num, true, sizeof(num));
    num[0] = num[1] = false;
    for(i = 4; i < N; i+= 2) num[i] = false;

    for(i = 3; i < N; i += 2) {
        if(num[i]) {
            k = i;
            while(k+i < N) {
                k += i;
                num[k] = false;
            }
        }
    }
}

void store()
{
    for(int i = 2; i < N; i++)
        if(num[i]) primes[total++] = i;
}

void prime_factorize(int n) // O(log n)
{
    ndiv = 0;
    for(int i = 0, j = sqrt(n); primes[i] <= j; i++) {
        if(n % primes[i] == 0) {
            while(n % primes[i] == 0) {
                n /= primes[i];
                divisors[ndiv++] = primes[i];
            }
            j = sqrt(n);
        }
    }

    if(n > 1) // n is prime
        divisors[ndiv++] = n;
}


int main()
{
    sieve();
    store();

    //for(int i = 0; i < 100; i++)
        //cout << primes[i] << " ";

    int n = 150;
    prime_factorize(n);
    for(int i = 0; i < ndiv; i++)
        cout << divisors[i] << " ";

    return 0;
}