### 1.7 Computing Factorials

The factorial of an integer is the product of that number and all of the positive integers smaller than it. Thus the factorial of 5, written 5!, is the product of 5*4*3*2*1, or 120. Example 1-7 shows a class, Factorial, that contains a method, factorial( ), that computes factorials. This class is not a program in its own right, but the method it defines can be used by other programs. The method itself is quite simple; we'll see several variations of it in the following sections. As an exercise, you might think about how you could rewrite this example using a while loop instead of a for loop.

##### Example 1-7. Factorial.java
```package je3.basics;
/**
* This class doesn't define a main( ) method, so it isn't a program by itself.
* It does define a useful method that we can use in other programs, though.
**/
public class Factorial {
/** Compute and return x!, the factorial of x */
public static int factorial(int x) {
if (x < 0) throw new IllegalArgumentException("x must be >= 0");
int fact = 1;
for(int i = 2; i <= x; i++)    // loop
fact *= i;                 // shorthand for: fact = fact * i;
return fact;
}
}```