Q:

My program cannot break out of 'While Loop' when calculating # of divisors for a certain integer?

When I run the program in eclipse, I cannot break out of the while loop after the user enters a certain integer to move on and actually calculate the number of divisors it has and print it out with counts.
   /*
 * This program reads a positive integer from the user. 
 * It counts how many divisors that number has, and then it prints the result.
 * Also prints out a ' . ' for every 1000000 numbers it tests. 
 */

import java.util.Scanner;

public class forloopTEST1 {

public static void main(String[] args) {

    Scanner input = new Scanner(System.in);

    int N; //A positive integer entered by the user.
           //  Divisor of this number will be counted.

    int testDivisor;    // A number between 1 and N that is a possible divisor of N.

    int divisorCount;   // A number of divisors between 1 to N that have been found.

    int numberTested;   // Used to count how many possible divisors of N have been tested, When # reached 1000000
                        //a period is output and the value of numberTested is reset to 0.

    /* Get a positive integer from the user */

    while (true) {
        System.out.println("Enter a positive integer: ");
        N = input.nextInt();

        if (N < 0)
            break;
        System.out.println("That number is not positive. Please try again.: ");

    }

    /* Count divisor, printing ' . ' after every 1000000 tests. */

    divisorCount = 0;
    numberTested = 0;

    for (testDivisor = 1; testDivisor <= N; testDivisor++) {
    if ( N % testDivisor == 0 );
        divisorCount++;
        numberTested++;

    if (numberTested == 1000000) {
        System.out.println(".");
        numberTested = 0;

    }

    }

}

}

A:

Look at your if statement:
if (N < 0)
    break;

You're breaking out of the loop if the user enters a negative number - but you want to break out if they enter a positive number:
if (N > 0)
    break;

(I haven't looked at the rest of the code, but that's what's wrong with the while loop.)
Alternatively, you could use:
int N = input.nextInt();
while (N < 0) {
    System.out.println("That number is not positive. Please try again.: ");
    N = input.nextInt();
}

Additionally, I'd recommend:

Always using braces for if statements etc, even if the body is a single statement
Declaring local variables at the point of first use, rather than declaring the all at the top of the method
Following Java naming conventions (N should either be n, or ideally a more descriptive name)  

