Return Biggest Prime Factor Of Given Number

One of our assignments this week was to make a program that when given a number it will return the biggest prime factor of that number. So for example if the program is given the number 15, the output is 3.

144 gives you 3 also.
17 gives you 17
21 gives you 7.

Anyways, after some time trying out various things and combining stuff i googled with my textbook I somehow stumbled upon a code that works. But I cannot for the life of me understand how it works. I think it has something to do with the inner loop and the outer loop. But I feel like i cant go on without understanding how it works.

Here is the code:

public class BiggestFactor {
public static void main( String[] args ) {
int N;
N = StdIn.readInt();
int n = N;

[Code] .....