A perfect number is an integer that is equal to the sum of all of its positive divisors, except itself. For example, 28 is a perfect number because $28=1+2+4+7+14$. Which of the following is a perfect number?
(A) 10
(B) 13
(C) 6
(D) 8
(E) 9
A perfect number is an integer that is equal to the sum of all of its positive divisors, except itself. For example, 28 is a perfect number because $28=1+2+4+7+14$. Which of the following is a perfect number?
(A) 10
(B) 13
(C) 6
(D) 8
(E) 9

## Solution

We must check each of the answers:

Number Positive divisors Sum of all positive divisors except itself

| (A) | 10 | $1,2,5,10$ | $1+2+5=8$ |
| :--- | :--- | :--- | :--- |
| (B) | 13 | 1,13 | 1 |
| (C) | 6 | $1,2,3,6$ | $1+2+3=6$ |
| (D) | 8 | $1,2,4,8$ | $1+2+4=7$ |
| (E) | 9 | $1,3,9$ | $1+3=4$ |

The only number from this set that is a perfect number is 6 . (Note that the next two perfect number bigger than 28 are 496 and 8128 .)

ANswer: (C)