A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. In other words, a perfect number is the sum of its proper factors, which are the factors of the number excluding the number itself. For example, 6 is a perfect number because its proper factors are 1, 2, and 3, and 1 + 2 + 3 = 6. Another example is 28, which has proper factors 1, 2, 4, 7, and 14, and 1 + 2 + 4 + 7 + 14 = 28. The smallest perfect number is 6.
Some key facts about perfect numbers include:
- Perfect numbers are a topic of study in number theory.
- All known perfect numbers are even.
- It is unknown whether odd perfect numbers exist.
- Euclid proved that any even perfect number can be represented by the formula N = 2^(p-1) x (2^p - 1), where p is a prime number and 2^p - 1 is a Mersenne prime.
Examples of perfect numbers include 6, 28, 496, and 8,128.
