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Examples of multiplicative functions include many functions of importance in number theory, such as:
* <math>\phi</math>(''n''): [[Euler's totient function]] <math>\phi</math>, counting the positive integers [[coprime]] to (but not bigger than) ''n''
* <math>\mu</math>(''n''): the [[Möbius function]], related to the number of prime factors of [[square-free integer|square-free]] numbers
* gcd(''n'',''k''): the [[greatest common divisor]] of ''n'' and ''k'', where ''k'' is a fixed integer.
* ''d''(''n''): the number of positive [[divisor]]s of ''n'',
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