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A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the nu

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by sambati » Tue Aug 04, 2020 1:57 pm

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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=61+2+3=6. Which of the following is also a perfect number?

A 12
B 20
C 28
D 48
E 60
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Re: A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to th

by Jay@ManhattanReview » Wed Aug 05, 2020 12:02 am
sambati wrote: ↑
Tue Aug 04, 2020 1:57 pm
 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=61+2+3=6. Which of the following is also a perfect number?

A 12
B 20
C 28
D 48
E 60
Let's take each number one by one.

A 12: The required factors are 1, 2, 3, 4, and 6, Their sum = 1 + 2 + 3 + 4 + 6 = 16 ≠ 12. Incorrect.
B 20: The required factors are 1, 2, 4, 5, and 10, Their sum = 1 + 2 + 4 + 5 + 10 = 22 ≠ 20. Incorrect.
C 28: The required factors are 1, 2, 4, 7, and 14, Their sum = 1 + 2 + 4 + 7 + 14 = 28 = 28. Correct.
D 48
E 60

Correct answer: C

Hope this helps!

-Jay
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