### 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