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 80
- The diagonals of a regular octagon divide it into 80 regions
- 80 is the smallest cubeful integer with a cubeful successor
- There are 80 four-digit primes which are concatenations of two-digit primes
- 80 is the smallest number that is diminished by taking its sum of letters (writing out its English name and adding the letters using a=1, b=2, c=3, ...) - EIGHTY = 5+9+7+8+20+25 = 74
- 80 is the smallest number n where n and n+1 are both products of 4 or more primes
- 80 is the smallest number that appears in its factorial three times
Common Properties of 80
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.