What Makes Six a Perfect Number?

SpikedMath.com::Perfect is a comic in which the number six says "leave me alone, you mean nothing to me" to the number zero and zero replies with "but you're perfect."

What makes 6 a perfect number?

By definition, a perfect number is a "positive integer that is the sum of its proper positive divisors." A proper divisor of a number evenly divides into a number (i.e. it is a factor of the number).

   proper divisors of 6 are:  1  2  3
   sum proper diviors of 6: 1 + 2 + 3 = 6
   6 is a perfect number

OEIS.org::id:A000396

Exercises
  1. Show that 28 is a perfect number.

  2. If the sum of the proper divisors of number is less than the number, then the number is considered deficient. Show that 27 is a deficient number.

  3. If the sum of the proper divisors of number is greater than the number, then the number is considered abundant. Show that 42 is an abundant number.


Creator: Gerald Thurman [gthurman@gmail.com]
Created: 30 December 2009

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