An abundant number is a positive integer for which the sum of all its proper divisors (factors) is greater than the number. For example, 12 is abundant because the sum of its proper divisors 1, 2, 3, 4, and 6 is greater than 12. 

A deficient number is a positive integer for which the sum of all its proper divisors (factors) is less than the number. An example of a deficient number is 9 because 3 + 1 < 9.

A perfect number is a positive integer for which the sum of all its proper divisors (factors) equals the number. An example of a perfect number is 6 because 2 + 3 + 1 = 6. 

This applet takes a positive integer and decides whether it is perfect, abundant, or deficient, based on the sum of its proper divisors. Just enter the number, then press the Calculate button. It's pretty simple!