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 108
- 108 is 3 hyperfactorial, that is the product of the first three numbers raised to themselves: 108 = 11 * 22 * 33
- 108 is the smallest number whose divisors contain every digit at least once
- 108 is the smallest n such that n-th Fibonacci number is divisible by n, n + 1 and n - 1
- The interior angles of an equilateral pentagon measure 108 degrees each
- A web page on 108: Why 108? Article on the symbolism of the number 108
Common Properties of 108
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.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.