# 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 480

- 480 is the smallest product abc such that (a+2)(b+2)(c+2) = 2abc (480 = 6*8*10 and 960 = 8*10*12)
- 480 is the smallest number such that when written in hexadecimal (1E0) looks like another number in scientific E notation
- 480 is the smallest integer area of an integer-sided triangle, where the lengths of two of the sides are cubes

## Common Properties of 480

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.