# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 360

- 360 is the number of degrees in a circle
- 360 is the largest number out of two (the other being 36) that have the same number of letters in its Roman representation as its double, triple, quadruple, quintuple, sextuple and septuple
- 360 is the smallest number with three distinct exponents in its prime factorization
- 360 is the smallest number which is a product of three positive integers with a minimal sum in more than one way (360 = 5*8*9 = 6*6*19, with the minimal sum of 22)

## Common Properties of 360

The number n is *abundant* if the sum of all its positive divisors except itself is more than n.

They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.

A positive integer greater than 1 that is not prime is called *composite*.

Composite numbers are opposite to prime numbers.

A number is *even* if it is divisible by 2.

Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.

The number n is *evil* if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

The number n is *practical* if all numbers strictly less than n are sums of distinct divisors of n.