Question

N is a perfect number. what is the ratio of the sum of the factors of N and N?​

Answer 1

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

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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