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Abstract: the Little Fermat theorem helps us to define congruence relation using the relatively primeness. Further divisibility rules help to create the highest powers of primes confirm the residues. This in turn helps to create Cartesian coordinate system of residues while any number n can have at most distinct residues. Using this residue system as the Cartesian coordinates, we can create concatenated strings formed from the ordered - tuple that follow all the properties of a commutative ring. If the system is created using the composite numbers, then there will be zero divisors and otherwise, the commutative ring will be a field under usual addition and usual multiplication at the powers of the primes. These tuples can be encoded using the technique of cross product of – length and decoded using the reverse cross product technique.