Loops.java

import java.io.*;
import java.util.*;

public class Loops {
    
    
    public int fact (int n) {
	    
	if (n > 1) {
	    return n * fact (n-1);
		}
	else 
	    return 1;	
    }
    
    public int fact2 (int n) {
	
	int result = 1;
	while (n > 1) {
	    result = result * n;
	    n = n - 1;
	}
	
	return result;	
    }
    
    public int gcd (int a, int b) {
	
	int c = Math.min (a, b);
	while (!(a % c == 0 && b % c == 0))
	    c = c - 1;
	
	return c;
    }
    
    public int gcd2 (int a, int b) {
	
	int c;
	while  (b > 0) {
	    c = b;
	    b = a % b;
	    a = c;
	}
	
	return a;
    }
    
    public boolean isPrime (int n) { //Tests if n is divisible by odd numbers between sqrt(n) and n/2, inclusive.
	
	int min = (int)(Math.ceil (Math.sqrt (n)));
	int max = n / 2;
	if (max == 1)
	    return true;
	if (n % min == 0 || n % max == 0)
	    return false;
	else {
	    if (min % 2 == 0) {
		min += 1;
	    }
	    while (min < max) {
		if (n % min == 0)
		    return false;
		min += 2;
	    }
	    return true;
	}
    }
}