To create a program that can calculate and determine the number of factor pairs of a given number, in a specified range of numbers.

In mathematics, you have likely encountered the notion of “prime” numbers, those values which are divisible only by 1 and the number itself.

Expanding our view on the situation, when considering factors of a number, we have the presence of a “factor pair”; ie a pair of two values that are evenly divisible into that number.

For 17, a prime number, we have just ONE factor pair: 1 and 17:

• 17 % 1 == 0
• 17 % 17 == 0

All other values (2-16) when we divide them into 17 results in a non-zero value for the remainder.

In this way, prime, or primary, numbers, have exactly ONE factor pair. To further simplify matters, we can call it an N-ary(1) or nary(1) value. Where the number indicates the number of factor pairs.

A secondary, or nary(2) number, on the other hand, has exactly TWO sets of factor pairs.

Take the number 6, for instance:

• factor pair of 1 and 6
• factor pair of 2 and 3

Where 17 was a primary number, 6 is a secondary number.

We are going to be exploring a basic, brute force, method of determining factors for a number, and that is the “trial by division” method.

Here, we successively divide a number by potential factors, to see if the factor evenly divides into the number. For convenience, we will assume the 1 and number factor pair, because EVERY number is evenly divisible by 1 and itself.

So, the number 5:

• 5 % 2 == 1
• 5 % 3 == 2
• 5 % 4 == 1

No other evenly divisible factors were found in the range 2-(N-1), therefore we are only left with the factor pair of 1 and N, making 5 an nary(1) value.

The number 14:

• 14 % 2 == 0 another factor!
• 14 % 3 == 2
• 14 % 4 == 2
• 14 % 5 == 4
• 14 % 6 == 2
• 14 % 7 == 0 another factor!
• 14 % 8 == 6
• 14 % 9 == 5
• 14 % 10 == 4
• 14 % 11 == 3
• 14 % 12 == 2
• 14 % 13 == 1

Because factor pairs ALWAYS come in a set of 2, we have the factor pairs of 1 and 14, along with 2 and 7.

How about 12:

• 12 % 2 == 0
• 12 % 3 == 0
• 12 % 4 == 0
• 12 % 5 == 2
• 12 % 6 == 0
• 12 % 7 == 5
• 12 % 8 == 4
• 12 % 9 == 3
• 12 % 10 == 2
• 12 % 11 == 1

There are 4 additional factors discovered here, giving us a total of 6 factors, or three factor pairs:

• 1, 12
• 2, 6
• 3, 4

Notice also how the factors are nested: 1 and 12 are the outermost, 2 and 6 are encapsulated within that, and inside there, 3 and 4.

Because there are 3 factor pairs, 12 would be considered an nary(3) value (or a tertiary number).

It is your task to write a program that, upon accepting various pieces of input from the command-line, computes the number of factor pairs of a given number or range of numbers, displaying to STDOUT all the numbers in that range that qualify as a nary number of the specification.

Your program should accept command-line arguments as follows:

$ ./cnv0 NARY START END

All are mandatory. If any are lacking or incorrect, display an error and exit with a non-zero value.

Your program should:

• have valid, descriptive variable names of length no shorter than 4 symbols
• have consistent, well-defined indentation (no less than 4 spaces per level of indentation)
  • all code within the same scope aligned to its indentation level
• have proximal comments explaining your rationale and what is going on, throughout your code
• to STDERR, prompt for the number (range appropriate of an unsigned long int)
  • properly store this in a variable of type unsigned long int
• process the arguments, check to make sure the numbers provided are positive numbers greater than or equal to 1 or 2 (depending); if in violation, display an error (to STDERR) and exit with a non-zero value.
  • the nary value must be a value greater than or equal to 1
  • the starting and ending values must be greater than or equal to 2
• proceed to evaluate the appropriate number range, determining whether or not it is an nary number as specified.
  • if it is, display the value to STDOUT in space-separated form (see execution section below for message)
  • if it is not, do not display anything related to that value (again, see execution section below)
• using a single return statement at the conclusion of the code, return a 0 indicating successful operation

Some additional points of consideration:

• Note that the driving variables in your loops need to be at least of type short int, otherwise you may get a warning when you compile it.

lab46:~/src/discrete/cnv0$ ./cnv0 2 3 12
4 6 8 9 10
lab46:~/src/discrete/cnv0$ 

The execution of the program is short and simple- obtain the input, do the processing, produce the output, and then terminate.

As we have been doing all along, use the following options to gcc when compiling:

lab46:~/src/discrete/cnv0$ gcc -Wall --std=gnu99 -o cnv0 cnv0.c
lab46:~/src/discrete/cnv0$ 

To successfully complete this project, the following criteria must be met:

• Code must compile cleanly (no notes, warnings, nor errors)
• Output must be correct, and match the form given in the sample output above.
• Code must be nicely and consistently indented
• Code must be well commented
• Do NOT double space your code. Group like statements together.
• Output Formatting (including spacing) of program must conform to the provided output (see above).
• Track/version the source code in a repository
• Submit a copy of your source code to me using the submit tool.

To submit this program to me using the submit tool, run the following command at your lab46 prompt:

$ submit discrete cnv0 cnv0.c
Submitting discrete project "cnv0":
    -> cnv0.c(OK)

SUCCESSFULLY SUBMITTED

You should get some sort of confirmation indicating successful submission if all went according to plan. If not, check for typos and or locational mismatches.

What I'll be looking for:

78:cnv0:final tally of results (78/78)
*:cnv0:proper error checking and status reporting performed [13/13]
*:cnv0:correct variable types and name lengths used [13/13]
*:cnv0:proper output formatting per specifications [13/13]
*:cnv0:runtime tests of submitted program succeed [13/13]
*:cnv0:no negative compiler messages for program [13/13]
*:cnv0:code is pushed to lab46 repository [13/13]

Additionally:

• Solutions not abiding by spirit of project will be subject to a 25% overall deduction
• Solutions not utilizing descriptive why and how comments will be subject to a 25% overall deduction
• Solutions not utilizing indentation to promote scope and clarity will be subject to a 25% overall deduction
• Solutions not organized and easy to read are subject to a 25% overall deduction