Question

Can someone help correct my algorithm? I’ve tested it on a few numbers, and it doesn’t output the complete factorization. For numbers with a large number of factors, it just completely fails.

int num = 20;

for(int i = 2; i <= num; i++)
{
    if(num%i == 0)
    {
        cout << i << endl;
        cout << num << endl;
        num = num/i;    
    }
}

EDIT: The two answers provided did not work, still not getting full results.

EDIT2: Divisors VS Factors

Answer 1

Judging from you comment to @Luchian Grigore, you’re confusing divisors with (prime) factorization. Divisors of a number are all numbers for which num % i == 0 is true. Factorization means getting a representation of num by a product of smaller numbers. If you want uniqueness of factorization, you usually use prime factorization.

To get all the divisors your code should be

for ( int i = 1; i <= num; ++i ) // note that 1 and num are both trivially divisors of num
{
    if ( num % i == 0 ) // only check for divisibility
    {
        std::cout << i << std::endl;
    }
}

to get the (prime) factorization, it’s

for ( int i = 2; i <= num; ++i )
{
    while ( num % i == 0 ) // check for divisibility
    {
        num /= i;
        std::cout << i << std::endl;
    }
    // at this point, i cannot be a divisor of the (possibly modified) num.
}