Prime Factors in C++

The prime factors of a number are all of the prime numbers that can be multiplied together to get the number.
Examples:
8=1*2*2*2
3=1*3
10=1*2*5
24=1*2*2*2*3
Your program should find the prime factors recursively. Find the first factor by trying the divisors
2,3,5,7,11,13, 15 (15 won't work because we already tried 3 and 5, but it is easier to count by 2's) . If no divisor works up to the square root, then the number is prime.
Lets see how we got the results for 24.
The user entered 24 and we printed "24=1*"
We call factors(24). In factors(24) we find the divisor 2 and print "2*" and then call factors(12).
In factors(12) we find the divisor 2 and print "2*" and then call factors(6).
In factors(6) we find the divisor 2 and print "2*" and then call factors(3).
In factors(3) we cannot find a divisor so we print "3" and end.

#include <iostream>

using namespace std;

void primeFactors(int num);

int main()
{
    int num;

    cout << "Please enter in the number that we want to find the prime factors of: ";
    cin >> num;
    cout << "Factors of " << num << " = ";
    primeFactors(num);
    cout << "\n";
    return 0;
}

void primeFactors(int num)
{
    int factor = 2;

    while(true)
    {...

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