How do you find perfect numbers below 30?

Answer 1

A perfect number is a whole number such that when you add up all of the factors less than that number, you get that number.

There are only two perfect numbers less than 30. The first one is 6 since 1+2+3-6 next we see that 1 + 2 + 4 + 7 + 14=28 so 28 is the only other perfect number below 30.

Euclid proved that 2p−1(2p−1) is an even perfect number whenever 2p−1 is prime.

This works for 6 and 28 where p is a prime and is 2 and 3 respectively. Using this formula for p=5, the next perfect number is 24(25−1) = 496

The next one is p = 7 where we have 26(27−1) = 8128.

The next perfect number is 33550336 we get this with the prime 13.