## Using objects as return values

1.
You are probably getting sick of the factorial method by now, but just for practice, write an iterative version of factorial. Put it in a new project named Big.prj.

2.
Print a table of the integers from 0 to 30 along with their factorials. At some point around 15, you will probably see that the answers are not right any more. Why not?

3.
Go to the Sun web page that contains all the Java documentation; there is a link to it from the class web page. Click on the java.math package and then click on the BigInteger class. Print the documentation of the BigInteger class. Read it.

BigIntegers are built-in objects that can represent arbitrarily-big integers. There is no upper bound except the limitations of memory size and processing speed.

4.
There are several ways to create a new BigInteger, but the one I recommend uses valueOf. The following code converts an integer to a BigInteger:

```    int x = 17;
BigInteger big = BigInteger.valueOf (x);
```
Type in this code and try out a few simple cases like creating a BigInteger and printing it. Notice that println knows how to print BigIntegers! Don't forget to add import java.math.BigInteger to the beginning of your program.

5.
Unfortunately, because BigIntegers are not primitive types, we cannot use the usual math operators on them. Instead we have to use object methods like add. In order to add two BigIntegers, you have to invoke add on one of the objects and pass the other as an argument. For example:

```    BigInteger small = BigInteger.valueOf (17);
BigInteger big = BigInteger.valueOf (1700000000);
```
Try out some of the other methods, like multiply and pow.

6.
Convert factorial so that it performs its calculation using BigIntegers, and then returns the BigInteger as a result. You can leave the parameter alone--it will still be an integer.

7.
Try printing the table again with your modified factorial function. Is it correct up to 30? How high can you make it go? On my machine, I calculated the factorial of all the numbers from 0 to 999, but it took over 2 minutes. The last number, 999!, has 2565 digits.