TheAlgorithms-C-Plus-Plus/Math/Prime_Factorization/primefactorization.cpp

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

// Declaring variables for maintaing prime numbers and to check whether a number is prime or not
bool isprime[1000006];
vector<int> prime_numbers;
vector<pair<int,int> > factors;

// Calculating prime number upto a given range
void SieveOfEratosthenes(int N)
{
	memset(isprime, true, sizeof isprime);
	
	for(int i=2; i<=N ;i++)
	{
		if(isprime[i])
		{
			for(int j=2*i; j<=N; j+=i)
			isprime[j]=false;
		}
	}
	
	for(int i=2;i<=N;i++)
	{
		if(isprime[i])
		prime_numbers.push_back(i);
	}
	
	return;
}

// Prime factorization of a number
void prime_factorization(int num)
{
	for(int i=0; prime_numbers[i]<=num; i++)
	{
		int count=0;
		
		while(num%prime_numbers[i] == 0)
		{
			count++;
			num = num/prime_numbers[i];
		}
		
		if(count)
		factors.push_back(make_pair(prime_numbers[i],count));
	}
	
	if(num>2)
	factors.push_back(make_pair(num,1));
	
	return;
}

int main()
{
	int num;
	cin>>num;
	
	SieveOfEratosthenes(num);
	
	prime_factorization(num);
	
	// Prime factors with their powers in the given number in new line
	for(auto it: factors)
	{
		cout<<it.first<<" "<<it.second<<endl;
	}
	
	return 0;
}