Trying to find the greatest prime factor of a number

Question

I'm a beginner programmer and I've just taken a challenge to find the greatest prime number of a very large number. But I've been trying to write a code to find a solution but I don't have any luck with it. This was my last attempt

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

int num = 100000;
int rem = 0;
int prime = 0;
boolean isPrime = true;
int j = 2;


for(int i = 1;i < num;++i) {       //Outer loop to find the factor of the num.
  rem = num % i;                   
  if((rem == 0)&&(i != 1)) {       //Checking if i is a factor.

    while((j <= i) && (isPrime)) { //Inner loop trying to find if i is prime.
      if((i % j) == 0) {           //Checking if i/j has any remainders.
        isPrime = false;           //If there isn't any remainders, i isn't
                                   //prime, isPrime, is false and exists the
                                   //inner loop.
      }
      else {                       //If i/j has any remainders, continue the
                                   //loop and print the value of i (a test).
        isPrime = true;            
        System.out.println(i);
        }
      ++j;                         //Increment j until inner loop condition  
      }                            //becomes false.
    }
  }
}
}

Answer 1

Several issues:

• You don't reset j back to 2 when you have a new value for i, which means you don't test for all divisors.
• You don't reset isPrime to false when you have a new value i;
• You let j reach the same value as i, which will always be considered a divisor, and so no value of i will be considered prime;
• You should not set isPrime to true just because you found one value of j that is not a divisor of i. You should only do that when none of the values of j divide i. So this you can only decide on after having considered all values of j;

Here is the suggested correction to your code:

int num = 100000;
int factor = 0;
int rem = 0;
int prime = 0;
boolean isPrime = true;
int j = 2;

for(int i = 1;i < num;++i) {
  rem = num % i;
  if((rem == 0)&&(i != 1)) {
    j = 2; // set j back to start
    isPrime = true; // assume prime before iterating
    while(j < i && isPrime) { // don't let j become equal to i
      if((i % j) == 0) {
        isPrime = false;
      } // don't set isPrime to true until you have completed all iterations
      ++j; 
    }
    if (isPrime) { // now is the time to check!
      prime = i; // remember this prime
    }
  }
}
// output result
System.out.println("largest prime divisor: " + prime);

Although this will work it is not optimal: you could stop looking for divisors j until the square root of i. And i should not have to increase further than the square root of num for the same reasons.