Division By Zero Error For Project Euler?

Question

I am trying to solve some project Euler problems and for whatever reason the following code gives me a division by zero error whenever I try to run it with large numbers. Can anyone tell me why?

import java.util.Scanner;

    public class Problem3LargestPrimeFactor {
        public static void main(String[] args) {
            Scanner input = new Scanner(System.in);

            System.out.println("Please enter the number to find the largest prime factor for.");
            long num = input.nextLong();
            int largest = 1;
            boolean isPrime = true;

            for(int i = 2; i < num; i++) {
                if(num % i == 0) {
                    for(int u = 2; u < i; u++){
                if(i % u == 0)
                    isPrime = false;
            }
            if(isPrime)
                largest = i;
            }
        }
    }
}

Now I'm aware that this is not the most efficient way to design the algorithm but can anyone tell me what is going on here?

Answer 1

You're overflowing int. In the loop for(int i = 2; i < num; i++), num is a long and i is only an int. When i reaches it's capacity, it wraps around to -2,147,483,648 and keeps being incremented until it gets to 0, at which point you get your error.

Answer 2

Other responses have already pointed out your error. Let me give you a better algorithm for factoring a composite integer using trial division. The basic idea is to simply iterate through the possible factors, reducing n each time you find one. Here's pseudocode:

function factors(n)
    f, fs := 2, {}
    while f * f <= n
        while n % f == 0
            append f to fs
            n := n / f
        f := f + 1
    if n > 1
        append n to fs
    return fs

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