Question

here is sample code

public static decimal factorization(decimal num, decimal factor)
        {

            if (num == 1)
            {
                return 1;
            }
            if ((num % factor)!= 0)
            {

                while(num% factor != 0)
                {
                    factor++;
                }

            }

            factors.Add(factorization(num / factor, factor));
            return factor;

        }

Note : I have initialize factors as global.

Above code will work fine for sample inputs 90 , 18991325453139 but will not work for input 12745267386521023 … so how can I do that ? How can I achieve this efficiently … I know recursive call will consume memory that’s why I have checked the last input using without recursion .. But its not working too

Answer 1

You can use that if

factor*factor > num

then num is prime

It will decrease complexity from O(n) to O(sqrt(n))

EDIT

while(num% factor != 0)
{
    factor++;
    if(factor*factor>num){ // You can precalc sqrt(num) if use big arifmetic
        factor=num; //skip factors between sqrt(num) and num;
    }
}