Check out example codes for "factorization in logn". It will help you in understanding the concepts better.

Code Example 1

#define MAXN   100001 
int spf[MAXN]; 

// Calculating SPF (Smallest Prime Factor) for every 
// number till MAXN. 
// Time Complexity : O(nloglogn) 
void sieve() 
{ 
    spf[1] = 1; 
    for (int i=2; i<MAXN; i++) 
  
        // marking smallest prime factor for every 
        // number to be itself. 
        spf[i] = i; 
  
    // separately marking spf for every even 
    // number as 2 
    for (int i=4; i<MAXN; i+=2) 
        spf[i] = 2; 
  
    for (int i=3; i*i<MAXN; i++) 
    { 
        // checking if i is prime 
        if (spf[i] == i) 
        { 
            // marking SPF for all numbers divisible by i 
            for (int j=i*i; j<MAXN; j+=i) 
  
                // marking spf[j] if it is not  
                // previously marked 
                if (spf[j]==j) 
                    spf[j] = i; 
        } 
    } 
} 
  
// A O(log n) function returning primefactorization 
// by dividing by smallest prime factor at every step 
vector<int> getFactorization(int x) 
{ 
    vector<int> ret; 
    while (x != 1) 
    { 
        ret.push_back(spf[x]); 
        x = x / spf[x]; 
    } 
    return ret; 
}

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