Abundant, Deficient, and Perfect

An abundant number is a positive integer in which the sum of all its factors, other than the number itself, is greater than the number. For example, 12 is abundant because the sum of its factors 1, 2, 3, 4, and 6 is greater than 12.

A deficient number is a number in which the sum of all its factors, other than the number itself, is less than the number. An example of a deficient number is 9 because 3 + 1 < 9.

A perfect number is a number in which the sum of all its factors, other than the number itself, equals the number. An example of a perfect number is 6 because 2 + 3 + 1 = 6.

Find all the abundant, deficient, and perfect numbers from 1 to 100. Using a table or a spreadsheet to conduct your investigation will be helpful. What patterns do you see? How many numbers less than 100 are perfect? Are there more abundant or deficient numbers? Are square numbers perfect? What about even numbers? Odd numbers?