# Perfect Numbers

Determine if a number is perfect, abundant, or deficient based on
Nicomachus' (60 - 120 CE) classification scheme for natural numbers.

The Greek mathematician [Nicomachus](https://en.wikipedia.org/wiki/Nicomachus) devised a classification scheme for natural numbers, identifying each as belonging uniquely to the categories of **perfect**, **abundant**, or **deficient** based on their [aliquot sum](https://en.wikipedia.org/wiki/Aliquot_sum). The aliquot sum is defined as the sum of the factors of a number not including the number itself. For example, the aliquot sum of 15 is (1 + 3 + 5) = 9

- **Perfect**: aliquot sum = number 
  - 6 is a perfect number because (1 + 2 + 3) = 6
  - 28 is a perfect number because (1 + 2 + 4 + 7 + 14) = 28
- **Abundant**: aliquot sum > number
  - 12 is an abundant number because (1 + 2 + 3 + 4 + 6) = 16
  - 24 is an abundant number because (1 + 2 + 3 + 4 + 6 + 8 + 12) = 36
- **Deficient**: aliquot sum < number
  - 8 is a deficient number because (1 + 2 + 4) = 7
  - Prime numbers are deficient
  
Implement a way to determine whether a given number is **perfect**. Depending on your language track, you may also need to implement a way to determine whether a given number is **abundant** or **deficient**.

## Setup

There are two different methods of getting set up to run the tests with Objective-C:

- Create an Xcode project with a test target which will run the tests.
- Use the ruby gem `objc` as a test runner utility.

Both are described in more detail here: http://exercism.io/languages/objective-c


### Submitting Exercises

When submitting an exercise, make sure your solution file is in the same directory as the test code.

For example, if you're submitting `Bob.m` for the Bob exercise, the submit command would be something like `exercism submit <path_to_exercism_dir>/objective-c/bob/Bob.m`.

## Source

Taken from Chapter 2 of Functional Thinking by Neal Ford. [http://shop.oreilly.com/product/0636920029687.do](http://shop.oreilly.com/product/0636920029687.do)

## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.