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Q.

Among the following,  a perfect number is

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a

14

b

6

c

27

d

56

answer is B.

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Detailed Solution

Perfect number: The sum of all its factors a given number  is equal to twice the number.

Option ( A ) : The factors of 14 are 1,2,7,14.

Sum of the factors of 14=1+2+7+14=24 .

 24 is not twice of the number14. So it is not a perfect number.

Option ( B ) : The factors of 6 are 1,2,3,6

Sum of the factors of  6=1+2+3+6=12

 12 is twice of the number 6. So it is a perfect number.

Option ( C ) : 27 is  not a perfect number

Option  ( D ) : The  factors of 56 are 1,2,4,7,8,14,28,56 

Sum of the factors of  56=1+2+4+7+8+14+28+56=120.

 120 is not twice of the number 56. So it is not a perfect number.

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Among the following,  a perfect number is