A number is called a perfect number if it equals the sum of all of its factors except itself. For instance, 6 is a perfect number because its factors are 1,2,3 and 6, and 1+2+3=6. What is the next greater perfect number?

Question

Pranav Tucker

Mathematics

23 April, 16:09

A number is called a perfect number if it equals the sum of all of its factors except itself. For instance, 6 is a perfect number because its factors are 1,2,3 and 6, and 1+2+3=6. What is the next greater perfect number?

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Answers (1)

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Elisa · Answer 1

28

Step-by-step explanation:

We know that,

A perfect number is a number which is the sum of all of its factors except itself.

Now, as we saw that the first perfect number is 6 because it is the sum of its divisors 1, 2 and 3.

So, we see that the next perfect number is 28.

Now, the divisors of 28 are given by 1, 2, 4, 7, 14 and 28.

Since, 28 = 1 + 2 + 4 + 7 + 14.

i. e. 28 is the sum of all of its divisors except 28 itself.

Thus, 28 is a perfect number.

Hence, the next perfect number is 28.