How to improve the algorithm for finding factors of a number?

Question

Java

Actually, the simplest task from the book is to improve the algorithm for finding all the numbers j, into which any number i is divisible without a remainder, except for itself.

public class Main {
  public static void main(String[] args) {

              for(int i=2; i <= 100; i++) {
                  System.out.print("Factors of " + i + ": ");
                  for (int j = 2; j < i; j++)
                      if ((i % j) == 0) {
                          System.out.print(j + " ");
                         // if (j == i/2) break;
                      }
                  System.out.println();
              }
  }
}

Actually, you need to reduce the number of iterations in the nested loop. My solution in the form of a documented line of code seems to work. The question is this: the solution seems too naive, because it was brought about by 'straight swotting'. Those. I looked at the result of the code, saw that the value of the number by which i is divided without a remainder never turns out to be more than 1 \ 2 from i and added such a line.
So, is there a less naive way, or a completely different one, which should be noted?

Answer 1

improvement 1 so as not to write an extra check in the for loop (int j = 2; j < i/2; j++)
Proving that this is correct is very easy. Let's assume that there is a divisor > j / 2. Divide and get the result < 2. Do not forget that formally the number is divisible by itself.
If you were interested in the simplicity of a number, and not the list of all its divisors, it would be enough to check up to the root of j. Which is also easy to prove by contradiction.