Project Euler > Problem 3 > Largest prime factor (Java Solution)

Problem:

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

Solution:

6857

Code:
The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}

/* 
 * Solution to Project Euler problem 3
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p003 implements EulerSolution {
 
 public static void main(String[] args) {
  System.out.println(new p003().run());
 }
 
 
 /* 
  * Algorithm: Divide out all the smallest prime factors except the last one.
  * For example, 1596 = 2 * 2 * 3 * 7 * 19. The algorithm ensures that the smallest factors will be found first.
  * After dividing out the smallest factors, the last factor to be found will be equal to the quotient, so it must be the largest prime factor.
  */
 public String run() {
  long n = 600851475143L;
  while (true) {
   long p = smallestFactor(n);
   if (p < n)
    n /= p;
   else
    return Long.toString(n);
  }
 }
 
 
 private static long smallestFactor(long n) {
  for (long i = 2, end = Library.sqrt(n); i <= end; i++) {
   if (n % i == 0)
    return i;
  }
  return n;  // Prime
 }
 
}