a question about remainders

[mepinoargote]

When a possitive integer is divided by 7, the only possible remainders are 0,1,2,3,4,5 and 6. Also, each of these remainders will occur exactly once when the terms in a sequence of 7 consecutive integers are divided by 7.

This is an explanation i got from OG about remainders, Can i generalize this rule when dividing a possitive integer by any n possitive integer? ex:

let´s say i divide a possitive integer by 12, are all possible remainders 0,1,2,3,4,5,6,7,8,9,10,11?

Thanks

[Ian Stewart]

Yes, when you divide by an integer n, the only possible remainders are 0, 1, 2, 3, ..., n-1. And when you divide each number in a set of n consecutive integers by n, you'll get each of these remainders exactly once. So if you, say, divide each number in a set of 12 consecutive integers by 12, you'll get (in some order) all of the possible remainders: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.