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Q.

Among the following , a perfect number is

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a

28

b

100

c

625

d

6

answer is A, B.

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Detailed Solution

Perfect number : Sum of factors of a given number is equal to twice of that number.

Option A)

Factors of 6=1,2,3,6

Sum of factors of  6=1+2+3+6

                                =12

    Twice the number=2(6)=12

Option B)

Factors of 28=1,2,4,7,14,28

Sum of factor of 28 =1+2+4+7+14+28

                                =56

Twice the number =2(28) =56

 6 and 28 are perfect numbers.

Option (c)

The factors of 100 are 1,2,4,5,10,20,25,50,100.

Sum of factors of 100=1+2+4+5+10+20+25+50+100=271

Twice the number =2(100) =200

 271 is not twice of the 100.

Option (d)

 The factors of 625 are 1,5,25,125,625.

Sum of factors of 625=1+5+25+125+625=781

Twice the number =2(625) =1250

781is not twice the625.

 Options c, d are not a perfect numbers.

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