# 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 252

- 252 is the smallest number which is the product of two distinct numbers that are reverses of each other: 252 = 12*21
- If you flip a coin 10 times in a row, there are exactly 252 ways in which it can turn out that you get exactly 5 heads and 5 tails
- 252 is the smallest palindrome with 5 prime factors (counted with multiplicity)
- 252 is the smallest average of an amicable pair

## Common Properties of 252

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.

A *palindrome* is a number that reads the same forward or backward.

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

*Undulating* numbers are numbers of the form abababab... in base 10.

This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.