COMP 170 (Sec. 008)    -    PROGRAM III

Sketch of ALGORITHM Prime Factorization:
 

Let n be the number whose prime decomposition is desired.

Test n for divisibility by 2.  If yes, then via a method call, determine the highest power, p, of 2 which evenly divides n.

Replace n by n / (2^p).

Test n for divisibility by 3.  If yes, then via a method call, determine the highest power, p, of 3 which evenly divides n.

Replace n by n / 3^p.

Test n for divisibility by 4, etc.

Continue until n = 1.
 

Sample dialogue:

Welcome to Jean Valjean's prime factorization program.

Please enter the integer:

1996

The prime decomposition of 1996 is:

  2 raised to the power 2

  499 raised to the power 1

Do you wish to continue?  If so enter Yes;  if not enter No:

Yes

Please enter the integer:

123456789
 
 

The prime decomposition of 123456789 is:

 3 raised to the power 2

 3607 raised to the power 1

 3803 raised to the power 1

Do you wish to continue?  If so enter Yes;  if not enter No: 

No

Thank you!
 
 
 

Extra credit:

(1)  In case n is actually prime, just print:  The number that you have chosen is prime.

(2)  Using the random number generator in the java Math class, give the user a chance to select her/his own integer or a random integer.
 

What to submit:

All of the following should be contained in a two-pocket folder with your name in large letters on
the outside of the folder.

•  Turn in a diskette with the code for the class containing your main method in the file PrimeFactorization.java and your other methods in the file Calculate.java.  Do not save these files in a directory.
•  A hard copy (print-out) of the source code for your program.  Include your name on the diskette. Always keep a back-up copy!

Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.

     -  Leohard Euler (1707-1783)