If the sum of the proper divisors of a number is equal to the number itself, then that number is called as a Perfect Number.
Perfect number n is given as n = s(n), where s(n) is the sum of the proper divisors or σ(n) = 2n where σ(n) is the sum of all the divisors.
It is not known whether there exists any odd perfect number or not.
Consider the number 6. The proper divisors of 6 are 1, 2, and 3. Sum of these divisors = 1 + 2 + 3 = 6. As the sum of the divisors is 6 and the number is also 6, so 6 is a perfect number.
A. 8
B. 28
C. 46
D. 58
Correct Answer: B
Step 1: A perfect number is equal to the sum of all its factors.
Step 2: The factors of 28 are 1, 2, 4, 7, and 14.
Step 3: Sum of the factors = 1 + 2 + 4 + 7 + 14 = 28
Step 4: So, according to the definition, 28 is a perfect number.
Q1: Which of the following is a perfect number?
Q2: Which of the following is NOT a proper divisor of 6?
Q: What are the first few perfect numbers?
A: The first four perfect numbers are 6, 28, 496, and 8128.
Q: Are there infinitely many perfect numbers?
A: It is unknown whether there are infinitely many perfect numbers, but it is known that every even perfect number can be written in the form 2^(p-1) * (2^p - 1), where 2^p - 1 is a Mersenne prime.