Question

Which of the following statements are true about the perfect numbers ?

• A. A number that equals the sum of its divisors
• B. A number that equals the sum of its divisors, excluding the number itself
• C. $6$ is a perfect number.
• D. A number that equals the sum of its factors, minus the number itself.

Answer 1

Answer: (B), (C), (D)

The correct options are
B A number that equals the sum of its divisors, excluding the number itself
C $6$ is a perfect number.
D A number that equals the sum of its factors, minus the number itself.

Perfect Number : A positive integer that is equal to sum of its divisiors, excluding the number itself.
Consider the number ${}^{\prime }{6}^{\prime }$.
Factors of ${}^{\prime }{6}^{\prime }$ are: 1, 2, 3, 6.
Now , on following the definition of a perfect number.
$\text{Sum of factors}=1+2+3+6-6=6(\text{that is number itself)}$
$\therefore 6\text{is a perfect number}$.