Given a positive integer , an integer is a totative of if . Put another way, all the smaller integers than that are coprime to are totatives of .

For example, the totatives of 21 are 1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19 and 20.

The count of totatives of is Euler's totient function . The set of totatives of forms a reduced residue system modulo . The word “totative” was coined by James Joseph Sylvester, who also coined “totient” (though despite occasional usage in some papers and books, the term “totative” has not caught on the way “totient” has).