Question

37. Following are perfect numbers-
(A) 6
(B) 28
(C) Both 6 and 28
(D) None of the above​

Answer 1

Answer:

(A) 6

Step-by-step explanation:

In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number

Answer 2

Answer:

C.) Both 6 and 28

Step-by-step explanation:

A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.

Factors of 6 (except 6) = 1, 2 and 3.

Now, for 6 to be a perfect no., 6 should be equal to the sum of its divisors.

=> 1 + 2 + 3 = 6

=> 6 = 6            (LHS = RHS)

So, 6 is a perfect number.

Factors of 28 (except 6) = 1, 2, 4, 7 and 14.

Now for 28 to be a perfect no., 28 should be equal to the sum of its divisors.

=> 28 = 1 + 2 + 4 + 7 + 14

=> 28 = 28        (LHS = RHS)

So, 28 is a perfect number.

Thus, both 6 and 28 are perfect numbers, making option C.) correct.