Divisor
Revision as of 22:59, 21 June 2006 by ComplexZeta (talk | contribs) (→Useful formulae: Replaced [...] by \lfloor...\rfloor)
Contents
[hide]Definition
Any natural number is called a divisor of a natural number if there is a natural number such that or, in other words, if is also a natural number. See Divisibility for more information.
Notation
A common notation to indicate a number is a divisor of another is n|k. This means that n divides k.
How many divisors does a number have
See main article, Counting divisors. If is the prime factorization of , then the number of different divisors of is given by the formula . It is often useful to know that this expression grows slower than any positive power of as . Another useful idea is that is odd if and only if is a perfect square.
Useful formulae
- If and are relatively prime, then