The current paper presents an algorithm of multiplication and division in the residual classes based on the theory of Galois fields GF(p). The use of Galois fields GF(p) to solve the problems of arithmetic multiplication and division eliminates a lot of limitations of existing algorithms. The advantage of the proposed algorithm is that it has no restrictions on the dividend and the divisor and it does not use the generalized positional notation and the expansion of the residue number systems.