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“Well, I hope at least some people got the joke, but I think an explanation will be needed for some.
Allow me to explain what a perfect number is. There are 3 types of NATURAL numbers (natural numbers are like 1, 2, 3, …): Abundant, deficient, and perfect.
So, you take a number, like 12, and you add all of its divisors that are smaller than it.
For 12, that’s 1,2,3,4,6.
Then add:
1+2+3+4+6=16
16>12, so,12 is an abundant number.
If it adds to less, then it is a deficient number, like 8
Divisors:1,2,4
1+2+4=7, 7<8, 8 is a deficient number.
Then there are the exteremely rare perfect numbers, like 6.
Divisors: 1,2,3
1+2+3=6
There are only thirty or so known perfect numbers, so they are rare indeed.
Anyway, hope you enjoyed this mini math lesson.”
Allow me to explain what a perfect number is. There are 3 types of NATURAL numbers (natural numbers are like 1, 2, 3, …): Abundant, deficient, and perfect.
So, you take a number, like 12, and you add all of its divisors that are smaller than it.
For 12, that’s 1,2,3,4,6.
Then add:
1+2+3+4+6=16
16>12, so,12 is an abundant number.
If it adds to less, then it is a deficient number, like 8
Divisors:1,2,4
1+2+4=7, 7<8, 8 is a deficient number.
Then there are the exteremely rare perfect numbers, like 6.
Divisors: 1,2,3
1+2+3=6
There are only thirty or so known perfect numbers, so they are rare indeed.
Anyway, hope you enjoyed this mini math lesson.”
If a number’s divisors sum to more than the number, it is abundant, and if less than the number, it is deficient.
To give one example of a use of such divisibility measures, abundant numbers are “very divisible.” That makes them a convenient number for things that might get broken into equal groups. The dozen is a good example, since it is abundant: 1+2+3+4+6 = 16>12. You can break a dozen things into halves, thirds, fourths, sixths, or twelfths.
23 = 6
47 = 28
815 = 240 is not perfect, because 15 isn’t prime
1631 = 496
etc.
We feel like there really ought not to be any odd perfect numbers – if any exist they’re extremely difficult to find – but technically we don’t know yet whether there are any.
Suck it, annoying classmate behind me moaning about “this will never have any application in my life”!
Me too. I feel like Twilight. :)