# Prime factors of a big number in C++

In this problem, we are given an integer N <= 10^18. Our task is to print all prime factors of the number along with there frequency of occurrence.

Let’s take an example to understand the problem,

Input: 100
Output: 2 2
5 2
Explanation: prime factorization of 100 = 2 * 2 * 5 * 5.

To solve this problem, we will have to find the prime factors of the number and then calculate their frequencies.

For this, we will find check the frequency of 2 as a factor and divide the number by 2. Then check from 3 to square root n. divide and increase the frequency of each prime number that is a factor of the number. And stop if the number becomes 1. Then print all primes with there frequencies.

The below code shows the implementation of our solution,

## Example

Live Demo

#include <iostream>
#include <math.h>
using namespace std;
void factorize(long long n){
int count = 0;
while (!(n % 2)) {
n/= 2;
count++;
}
if (count)
cout<<2<<"\t"<<count<<endl;
for (long long i = 3; i <= sqrt(n); i += 2) {
count = 0;
while (n % i == 0) {
count++;
n = n / i;
}
if (count)
cout<<i<<"\t"<<count<<endl;
}
if (n > 2)
cout<<n<<"\t"<<1<<endl;
}
int main() {
long long N = 21000;
cout<<"The prime factors and their frequencies of the number "<<N<<" are \n";
factorize(N);
return 0;
}

## Output

The prime factors and their frequencies of the number 21000 are
2   3
3   1
5   3
7   1