Prime factorization

#include<iostream>
#include<cmath> // sqrt()
using namespace std;

// This program displays the specified positive integer as
// the product of its prime factors.
// The integer must be in the range 2 - 2147483647
void display_prime_factors(int integer)
{
    // The integer is a sequence of prime numbers, some
    // are repeated, some are not.
    int factor_count = 0; // Count the occurence of each factor.

    bool factor_found = false; // No factor has been found yet. (This is for formatting.)

    // First count the number of factors of 2
    while (integer % 2 == 0) // If the integer is divisible by 2,
    {
        factor_count++; // Count one factor of 2.
        integer /= 2; // Remove that factor from the integer.
    }

    if (factor_count) factor_found = true; // If a factor was found, indicate it.

    // If there were more than one factors of two,
    // display 2 with exponent notation and the number of occurences,
    // then a multiplication sign for the next factor.
    if (factor_count > 1)
    {
        cout << "2^" << factor_count;
    }

    // If there was only one factor of 2, just display the 2.
    else if (factor_count == 1)
    {
        cout << "2";
    }

    // Now that all the factors of 2 are removed from the integer,
    // the rest of the factors in the remaining integer must be odd numbers.
    // We only need to check for all odd numbers less than or equal to the square
    // root of the integer, because the "greater than" side of the square root
    // has all the same factors as the "less than" side.
    for (int i = 3; i <= sqrt(integer); i += 2) // For odd numbers less than or equal to the square root
    {
        factor_count = 0; // Reset the factor count.
        while (integer % i == 0) // If the integer is divisible by the current odd number,
        {
            factor_count++; // Count that odd number as a factor.
            integer /= i; // Remove the factor from the integer.
        }
        // If there is a new odd factor and this is not the first
        // factor found, we need a multiplication sign in front.
        if (factor_count && factor_found) cout << " * ";
        // If there is a new odd factor and this is the first factor found,
        // indicate a factor was found (needed for future formatting).
        if (factor_count && !factor_found) factor_found = true;
        // If the factor occurs more than once, use exponent notation.
        if (factor_count > 1)
        {
           cout << i << "^" << factor_count;
        }

        // If there was only one occurence of the odd number, display the number.
        else if (factor_count == 1)
        {
            cout << i;
        }
    }

    // If the remaining integer is greater than one, it means
    // it is a prime number.
    if (integer > 1)
    {
        if (factor_found) cout << " * "; // If there's a factor before it, add a multiplication sign
        cout << integer << "\n";
    }
    cout << "\n"; // Go to the next line.
}

int main() {

    int number = 0; // The number to break into prime factors.
    cout << "This program expresses a positive integer as\n"
        "a product of prime factors.\n\n";
    cout << "Enter an integer : ";
    cin >> number; // Get the user's number.
    while ((number < 2) || (number > 2147483647)) // If the user's input is not within the range of an int,
    {
        cout << "Please enter a number in the range of 2 - 2147483647\n\n";
        cout << "Enter an integer : ";
        cin >> number; // Get new input.
    }

    cout << number <<  " =\n"; // Announce the result.
    display_prime_factors(number); // Display the result.
    cout << "\n"; // Go to the next line.
    return 0; // End the program.
}