数字 600851475143（Java）的最大质因数是多少？ 我的错误可能是什么？

Question

The code works just fine for the int data type, but 600851475143 seems to be too big of a number. How can I make it work? It just keeps running and never gives me an answer.

public class Main {
    public static void main(String[] args) {
       long a = 600851475143L;
        boolean prime = false;
        long big = 0L;
        for (long i = 1L; i < a; i++){
            if (a % i == 0){
                for (int j = 2; j < i/(float)2; j++){
                    if (i % j == 0){
                        prime = true;
                        break;
                    }
                }
                if(!prime){
                    big = i;
                }
            }
        }
        System.out.println(big);
    }
}

Answer 1

You need to use a long also for j .

Your variable naming is also a bit misleading: prime is true when the number is not a prime...

Answer 2

Your code has a lot of problems. My first advice would be to write clean and concise code with well-named variables. Secondly, analyze the runtime complexity of your program even if it works fast for large inputs. The fact that you run an inner loop inside if(a % i == 0) condition, makes your program extremely inefficient.

Here I provide a refactored version of your code with runtime complexity and good variable names in mind:

  public static void main(String[] args) {
    System.out.println(largestPrimeFactorOf(600851475143L));
  }

  public static long largestPrimeFactorOf(long input)
  {
    List<Long> factors = new ArrayList<>();
    // You start from 2, as 1 is not a prime number and also using 1 will cause an infinite loop
    for (long i = 2L; i < input; i++) {
      if (input % i == 0) {
        factors.add(i);
        while (input % i == 0) {
          input /= i;
        }
      }
    }

    // As we always add a bigger number to the factor list, the last element is the greatest factor.
    return factors.get(factors.size() - 1);
  }

Denote that this program will still be slow when the input is a large prime number, eg 100000000019. To handle such cases efficiently, it's better to use an efficient primality test algorithm. You can search the web for that. https://en.wikipedia.org/wiki/Primality_test