So 28/6. The interesting thing is that they are both what are called perfect numbers. Now you might already know what perfect numbers are, or can read the earlier wikipedia link, but let me try to explain, just to increase the length of this post. The idea is to first collect all the divisors of a number (except the number itself, these are called Proper divisors). Why, you might ask. There are many answers, because we can (from TBBT), or because I chose to (from Neo). So Just do it (Nike :p). To take an example, let's say the number is 10. So the divisors are 1,2,5. Add them together. So 1+2+5 = 8. Now this sum is less than our number. Such numbers are called deficient numbers. It also happens that in some cases the sum exceeds the number. For example, 12. Divisors of 12 are 1,2,3,4,6. So sum of divisors is 1+2+3+4+6 = 16, which is greater than 12. Such numbers are called abundant numbers. But a third possibility exists, and you might already have guessed it. A case where the sum of the proper divisors of a number is equal to the number. This is the thing we were after, the perfect numbers. See for yourself.
For 6, proper divisors are 1,2,3. Sum = 1+2+3 = 6
For 28, proper divisors are 1,2,4,7,14. Sum = 1+2+4+7+14 = 28
Enjoy!!
For 6, proper divisors are 1,2,3. Sum = 1+2+3 = 6
For 28, proper divisors are 1,2,4,7,14. Sum = 1+2+4+7+14 = 28
Enjoy!!
4 comments:
Perfect numbers are something that I have never seemed to fathom ... if the number in questions itself is not a divisor, then why is 1 spared of the same logic ... every number is divisible by 1 ... so it doesnt make sense to count 1 as a factor ... and if it does then the number itself should also be counted as a factor ... which will make a mockery of the concept of perfect numbers ... but theek hai ... Math is always searching for trends ... Cheers ... !!
Well we sum the proper divisors.. that does not include the number itself..
now it can be asked why the proper divisors are defined that way.. but I think the important thing to remember is that in math there are concepts defined in a particular way and we see what can be said using these.. the formalist philosophy of math takes this to great extremes but in the end it's the study of patterns..
This is interesting.. I never calculated it..
Isiliye to maine kiya na ;-)..
Cheers you have a perfect birthday :-)...
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