Intro to Computer Science


Additive and Multiplicative Persistence

Code due by Feb 23rd at 9:00 AM


The aim of this project is practice the use of while loops and conditionals statements within a project that is a little bit bigger than ones you have been working on.  This will give you some practice with Program Development.  Take the time to really think about this problem and work through the process before you begin to code.  Write small snippets of code to make sure you can perform smaller pieces of the assignment rather than jumping in and writing the whole program at once.

Quick Overview

You are going to write a program that prompts the user for an integer and then determines the additive persistence and corresponding additive root, and the multiplicative persistence, the corresponding multiplicative digital root of that integer. You will continue to do so until the user quits.

Additive Persistence

Additive persistence ( is a property of the sum of the digits of an integer. The sum of the digits is found, and then the summation of digits is performed on the sum, repeating until a single integer digit is reached. The number of such cycles is that integer’s additive persistence. Consider the following example:

1. The beginning integer is 1234
2. Sum its digits is 1+2+3+4 = 10
3. The integer is now 10
4. The sum of its digits is 1 + 0 = 1
5. The integer is 1. When the value reaches a single digit, we are finished. This final integer is the additive root

The number of cycles is the additive persistence. The integer 1234 has an additive persistence of 2 (first sum was 10, then the second sum was 1). The final digit reached is called the integer’s additive digital root. The additive digital root of 1234 is 1.


Multiplicative Persistence

The multiplicative persistence ( )and resulting multiplicative root are determined the same way, only multiplying the digits of an integer instead of adding. For example

1. The beginning integer is 1234
2. The product of 1*2*3*4 = 24
3. The integer is now 24
4. The product of 2*4 = 8
5. The integer is now 8. When the value reaches a single digit, we are finished. This final integer is the multiplicative root.

As before, the number of cycles is the multiplicative persistence. For 1234, the multiplicative persistence is 2, and its multiplicative root is 8.


Program Specification

In a file named you should write a program that runs as follows:

  1. Ask the user for an integer.
  2. If the integer is less than 0, that is a signal to quit the program.
  3. If the given integer is a single digit, report it’s additive persistence and multiplicative persistence as 0 and both its additive and multiplicative root as itself.
  4. If the given integer is more than a single digit, find the additive/multiplicative persistence and additive/multiplicative root of the given integer and report the results to the user
  5. If the value was non-negative continue by prompting the user until they quit.

Getting Started

  1. Start by understanding the process. Go through the examples in this program specification with paper and pencil, and also try it with new numbers.
  2. Use what you learned about the process to write a design document. You might want to write your document in bullited form that almost resembes code (and not a big paragraph). To start, break the problem into parts. Some parts (but not all) that will be needed are:
  3. Create the as usual.
  4. Use the design document for code comments and to write small pieces of your code at a time.
  5. Test each piece before moving on to the next.
  6. Get the whole thing to work with one or the other (additive, multiplicative) before you address the other.
  7. How do you get the digits of an integer? Look at this code for an example.
  8. FOR DEVELOPMENT PURPOSES ONLY, I would add some “diagnostic output” so you can be sure things are working as they should. For example, for each pass through the loop of the additive (or multiplicative) persistence, print each new integer created.  This should be removed before you make your final submission.

Example during development:

Note that the cycles demonstrate the use of “diagnostic output” (see (4) under “Getting Started”). Your final program should not print out such diagnostic output.


Example of final deliverable:

Final Submission

To upload your homework for grading, log on to eLearning, select this class, and navigate to the "Assignment Submissions" area. Click on the "Programming Assignment 4" folder and upload the python file named in its designated location.