Divisor
A 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 (i.e
divides
). See Divisibility for more information.
Notation
A common notation to indicate a number is a divisor of another is . This means that
divides
.
See the main article on 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
.
We also know that the product of the divisors of any integer
is
Another useful idea is that
is odd if and only if
is a perfect square.
Useful formulas
- If
and
are relatively prime, then