22. N is a perfect number. What is the ratio of the sum
of the factors of N to N?
(A) 1 (B) 2. (C) 3
(D) 4
Answers
Given : N is a perfect number.
To Find : The ratio of the sum of the factor of N and N
Solution:
A Perfect Number is a positive integer which is equal to the sum of its Proper divisors/factors.
Perfect number is a number that is sum of all of its positive divisors ( excluding itself )
Perfect number is a number that is half the sum of all of its positive divisors ( including itself )
N is a perfect number
Sum of the factor of N = N + N = 2N
ratio of the sum of the factor of N and N = 2N/N = 2
correct option B) 2
for example 6 is a perfect number
proper divisors 1 , 2 , 3
Sum = 1 + 2 + 3 = 6 = Number
Factors 1 , 2 , 3 , 6
Sum of Factors = 1 + 2 + 3 + 6 = 12
12/6 = 2
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