Why 21 is not a perfect number?

Answer 1

First, you want to know the definition of a perfect number:

A perfect number is an integer which is equal to the sum of all its positive integer divisors that are less than itself.

Example: The positive integer divisors of 6, less than 6, are 1, 2, and 3. The sum of those divisors is 1 + 2 + 3 = 6. Therefore, 6 is a perfect number.

Now, 21 does not meet this definition and therefore is not a perfect number.

Let's try it. There are three positive divisors of 21, namely, 1, 3, and 7, that are less than 21, itself. (There are no others.) But the sum of these divisors is

1 + 3 + 7 = 11, which is not equal to 21. Therefore, we confirm that 21 is not a perfect number.