Bunuel wrote:
A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and \(1 + 2 + 3 = 6\). Which of the following is also a perfect number?
A. 12
B. 20
C. 28
D. 48
E. 60
This is question is simple to calculate for all , To calculate sum of factors except the number , we calculate sum of all factors - the number.
Sum of all factors of a number is given by if a number is P= a^n * b^m * c^k. Sum of all factors of P = (1 + a ..... a^n) (1+b+b^2 .... b^m )(1+c + c^2+....c^k)
so 28 will have (1+ 2 + 4) (1+ 7) = 56 sum of factors ,excluding number will be 28, so the perfect number.
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