2.Prime factorization O(sqrt(N)).cpp

 #include <bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp>

#include <ext/pb_ds/tree_policy.hpp>

using namespace std;

using namespace __gnu_pbds;

template <class type1>

#define ll long long int

#define endl "\n"

#define ordered_set tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update>

using ordered_multiset = tree <type1, null_type, less_equal <type1>, rb_tree_tag, tree_order_statistics_node_update>;

 //ordered_multiset <ll> kek;(declaration for multiorder set)

// ordered_set o_set;(declaration)

//kek.order_of_key(i);(strictly less then i for multi order set)

//o_set.order_of_key(5) ;(strictly less then i for multi order set)

#define yes cout << "YES\n"

#define no cout << "NO\n"

int main()

{

    ios_base::sync_with_stdio(0);

    cin.tie(0);

    cout.tie(0);

   

    ll n,i,cnt;

    cin>>n;

    cnt=0;

    for(i=2;i*i<=n;i++)

    {

        if(n%i==0)

        {

             cnt=0;

             while(n%i==0)

             {

                 cnt++;

                 n/=i;

             }

             cout<<i<<"^"<<cnt<<endl;

        }

    }

    if(n>1)

    {

        cout<<n<<"^"<<1<<endl;

    }

    return 0;

}