Most people, and many computer professionals, have never heard of residue arithmetic. I do not propose to provide a background in that complicated subject here. The details of residue arithmetic can be found in some elementary number theory texts. I do think it's appropriate to recite a few basic facts about residue arithmetic. The binary, decimal, and hexadecimal number systems are all examples of polynomial number systems. Their successive radices are formed by powers of the number base‑‑2, 10, or 16. The radices of the familiar decimal system are 1, 10, 10 squared, 10 cubed etc.
The successive radices of residue number systems are formed from a set of mutually prime numbers, or any set of numbers that have no common divisor. 7 & 8 are mutually prime, but 4 & 6 are not because they are both divisible by 2. These numbers are usually called modules and the range of any particular residue number system is the product of all its modules.