A perfect number is defined as a positive integer which is the sum of its proper positive factors, that is, the sum of the positive divisors excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself).

The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors and \(1 + 2 + 3 = 6\). Equivalently, the number 6 is equal to half the sum of all its positive divisors: \(\left[ {\frac{{1 + 2 + 3 + 6}}{2}} \right] = 6\).

The next perfect number is 28. As 28 can be written as \(= 1 + 2 + 4 + 7 + 14\). This is followed by the perfect numbers 496 and 8128.

How to find a Perfect Number:

If \({2^n} - 1\) is a prime number then the formula \({2^{n - 1}}({2^n} - 1)\) always give an even perfect number.  For example the first four perfect numbers can be obtained by putting 

\(n = 2\):   \({2^1}({2^2} - 1) = 6\)

\(n = 3\):   \({2^2}({2^3} - 1) = 28\) 

\(n = 5\):   \({2^4}({2^5} - 1) = 496\)

\(n = 7\):   \({2^6}({2^7} - 1) = 8128\)

But the fifth perfect number not be obtained by putting \(n=11\), the value \({2^{11}} - 1 = 2047 = 23 \times 89\) is not prime and therefore n = 11 does not yield a perfect number. 

The fifth perfect number 33550336 

\( = \left[ {{2^{12}}({2^{13}} - 1)} \right]\) has 8 digits.

It is important to note that:

Sum of proper factors of a perfect number is always equal to the number itself.
Sum of reciprocal of factors of a perfect number is always 2.