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 24
- 24 is the only number that is the product of all the numbers less than its square root
- 24 divides the difference between any two prime squares greater than three
- The diagonals of a regular hexagon divide it into 24 regions
- Subtracting one from each of its divisors (except 1 and 2, but including itself) yields a prime number - 24 is the largest number with this property
- 24 is the smallest abundant factorial
Rare Properties of 24
The n-th compositorial is the product of the first n composite numbers.
Compositorial numbers are factorials divided by primorials.
The n-th factorial is the product of the first n natural numbers.
The factorial deserved an exclamation mark for its notation: k! = 1*2*3*...*k.
Common Properties of 24
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.