Weed Out All Prime Numbers Without Using Any Kind Of Division?

The challenge is to weed out all the prime numbers without using any kind of division (%, /). My code doesn't weed out certain numbers, such as many multiples of 5, the number 49, etc, and I am not sure why. Here is my code.

My logic for the for loops was this: Starting with the upper numbers of the ArrayList, find every number that is a multiple of that number and remove it from the ArrayList. Every time you find a multiple, increase the variable multiply, so the program knows what the next multiple to look for.

// program doesn't work yet.
import java.util.ArrayList;
// import java.util.ListIterator;

public class Sieve2
{
public static void main(String[] args)
{
int upperLimit = 55;
ArrayList<Integer> primes = new ArrayList<Integer>();

[Code] .....

And this is the output:

1 2 3 5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55