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.
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.
- If and are relatively prime, then