This number is just too perfect!

Number Theory Level 3

The answer to this question is a 2-digit positive integer the sum of whose proper divisors happens to equal itself. What is the answer to this question?


The answer is 28.

Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Matt Mcc
Aug 19, 2016

What this question is asking for is essentially a 2 digit perfect number.

You can find it when the sum of its proper divisors is equal to the number itself.

28 is the only positive 2 digit number that meets this criteria.

1,2,4,7,14 are its proper divisors.

1 + 2 + 4 + 7 + 14 = 28 \boxed{1+2+4+7+14=28}

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28 is the only positive 2 digit number that meets this criteria.

Got a proof?

Pi Han Goh - 4 years, 10 months ago

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Here is the tedious route. If we check every 2 digit number, we can find that the only 2 digit perfect number is 28.

Goh Choon Aik - 4 years, 9 months ago

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