## Perfect Number

What are the values of a and b?
I. a and b are prime numbers and a is greater than b.
II. Their product is a perfect number i.e. the sum of all the factors of the product add up to the product itself.
I would like to know if we can derive such number with the help of the 2 conditions given.
Thanks in advance.

## Oops!Even after trying for

Oops!
Even after trying for more than 15 minutes I couldnâ€™t find a single number
Is there any such number exists
anyway nice Qs

## First let me explain a bit

First let me explain a bit about perfect number
A perfect number N is equal to the sum of its divisors (where the divisors include 1, but not N itself).
Example 6, divisors are 1 x 6 and 2 x 3 so we have 3 divisors except the number i. e. 1 , 2 and 3 and the sum of the three numbers are 1 + 2 + 3 = 6
Another number is 28 = 1 + 2 + 4 + 7 + 14.
6 is the first perfect number and the first three perfect numbers are: 6, 28 and 496
So formally we can define a perfect number as
"A perfect number is as an integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number"
**Properties of Perfect Numbers**
1. Though technically we cant say that no odd perfect number exist but in reality you will never come across any such number.
2. Exhaustive computer search has shown that there are no odd perfect numbers less than 10300.
3. Euler Principle : all even perfect numbers are of the form 2^{(p-1)}(2^{p}-1)
6 = 2 (2^{2}-1), 28= 2^{2} (2^{3}-1), 496 = 2^{4} (2^{5}-1)
4. Every even perfect number ends in a '6' or an '8'.
Now coming back to your question:
The values of a and b can be 3 & 2, 7 & 4
But how many? I donâ€™t think it can be answered because till now we donâ€™t know how many perfect numbers exists. (About 30 are know till now)
This sort of questions can come in CAT but there you will have multiple answers to choose from and such questions should be tackled by looking the answers
From where you got such a nice question.

## RE:Properties of Perfect Numbers

Great srikanth,
That's a nice research on perfect numbers.
This problem is taken from http://www. tenaday.co.in
But the thing is it was asked in DI section. I think by this time you should have understood what sort of question it is.
1. Question can be answered using any one statement alone.
2. Can be answered using either statement alone.
3. Can be answered using both the statements together.
4. Cannot be answered using both the statements.
So, it is not like we can choose from the set of options that are given below.
Anyway, Thanks for the concept Srikanth.

## Ok the obvious answer is d

Ok the obvious answer is d â€“ cant be determined and the reason is as given in my previous message.
Btw srikant here not srikanth