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n excluding n itself

by sanju09 » Sat Mar 06, 2010 6:07 am
If the sum of the divisors of a positive integer n excluding n itself is equal to n, then n is called a Perfect Number. Which of the following is NOT a Perfect Number?
(A) 6
(B) 28
(C) 124
(D) 496
(E) 8128
Last edited by sanju09 on Sat Mar 06, 2010 6:26 am, edited 1 time in total.
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by rohan_vus » Sat Mar 06, 2010 6:25 am
Should be A

Trying with 4 gives 1 and 2 as possible factors and it tells that 4 is not a perfect number

Sum of all factors of a perfect square (say n ) including n istelf is always odd . So sum of all factors factors excluding n is also always odd if n is even

So a even perfect square is never a perfect number .
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by sanju09 » Sat Mar 06, 2010 6:27 am
rohan_vus wrote:Should be A

Trying with 4 gives 1 and 2 as possible factors and it tells that 4 is not a perfect number

Sum of all factors of a perfect square (say n ) including n istelf is always odd . So sum of all factors factors excluding n is also always odd.

So a perfect square is never a perfect number .
Please see it again as I have edited it in the meanwhile, sorry for inconvenience.
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by rohan_vus » Sat Mar 06, 2010 6:39 am
In that case C should be the one

[spoiler]124 has factors 1,2,4,31,62 -->sum = 100 ( not equal to 124)[/spoiler]
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