What is a perfect number and what is the smallest perfect number?

Answer 1

A perfect number is one where the sum of the factors of a number adds up to that same number. For example, the factors that go evenly into 28 are 1, 2, 4, 7, and 14. 1+2+4+7+14 = 28, so 28 is therefore considered a perfect number. All the perfect numbers that we know of are of the form 2^n-1 * 2^(n-1), where n is a prime number. Not all prime numbers will generate perfect numbers in this way, but some will. For example

--- 2^3-1 * 2^(3-1) = 8-1 * 2^2 = 7*4 = 28

The smallest perfect number is 6 (1+2+3).

--- 2^2-1 * 2^(2-1) = 4-1 * 2^1 = 3*2 = 6

Answer 2

6 is the smallest

Then 28, 496, 8128

In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors.

Interesting fact is the last digit of any even perfect number must be 6 or 8

Answer 3

a number whose divisors add up the the number. example
1+2+3=6
6 is the smallest perfect number.

Answer 4

7

Answer 5

Addition to Kyrix's correct answer: it has been proven that any even perfect number has the Mersenne form

2^n . [2^(n+1)-1], with the last factor prime

Odd perfect numbers are not known, and if they exist they must have more than 300 digits, at least 8 different prime factors, one of which with 20 digits or more.

Answer 6

A perfect number is a number is when if you take the factors of the number and add them it gets the same number, I think.

6 is the smallest one. Jeesh, you guys are all wrong!

Answer 7

21 or 18