If a number’s proper divisors (the divisors other than the number itself) add up to the number itself, we call the number perfect (partly because this is SO rare!).  Examples: 6 is perfect, since its proper divisors are 1, 2, & 3 and 1 + 2 + 3 = 6.  28 is perfect because the proper divisors are 1,2,4,7, and 14, and these add to 28.

Interesting Facts about perfect numbers:

*The first 4 perfect numbers are 6, 28, 496, and 8128.  These 4 were known to the anient Greeks.
*There are currently only 50 known perfect numbers.  (Many of them are HUGE.)  All of them are even.  
*It can be proven that all (even) perfect numbers end in 6 or 8.
*No one knows if there are any odd perfect numbers.  (Find one, and make us both famous.  :-)).
*One of the most amazing coincidences in all of mathematics is the perfect numbers are directly linked to Mersenne Primes.  But that is a story for another day.