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# If perfect numbers are defined as numbers whose all the factors sum up

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If perfect numbers are defined as numbers whose all the factors sum up  [#permalink]

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30 Jun 2017, 20:36
1
2
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:09) correct 39% (01:56) wrong based on 113 sessions

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If perfect numbers are defined as numbers whose all the factors sum up to twice the number then Which of the following is/are perfect number(s)?

I) 6
II) 28
III) 36

A) I only
B) II only
C) III only
D) I and II only
E) I, II and III all

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If perfect numbers are defined as numbers whose all the factors sum up  [#permalink]

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30 Jun 2017, 23:00
1
Definition : If sum of all factors is twice the number, then the number is a perfect number

Evaluating the options
I) 6 has 4 factors(1,2,3 and 6) - The sum of the factors is 12(twice the number 6)
Hence, this number is a perfect number,
II) 28 has 6 factors(1,2,4,7,14,28) - The sum of the factors is 56(twice the number 28)
Hence, this number is a perfect number
III) 36 has 9 factors(1,2,3,4,6,9,12,18,36) - The sum of the factors is 91(which is not twice the number 36)
Hence, this number is not a perfect number

I and II only are the perfect numbers, and Option D is the correct answer
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Re: If perfect numbers are defined as numbers whose all the factors sum up  [#permalink]

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17 Jan 2019, 05:38
In the case of 36: Is 6 considered as factor once or twice (as 6*6=36)?
Re: If perfect numbers are defined as numbers whose all the factors sum up   [#permalink] 17 Jan 2019, 05:38
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