FIELD: information technology. ! SUBSTANCE: apparatus for generating remainder for given modulo contains T units for generating partial remainders with a data input on n bits, an input for primary remainders on (n-p-1)·(p+1) bits, an initialisation input, a synchronous input and output on (p+q) bits, respectively, two parallel (p+2)- and (p+1)-bit registers with a synchronous input, a data input and output, respectively, a multiplexer with two data inputs, a control input and output, a comparator with two inputs and an output, a subtractor with minuend and subtrahend inputs, as well as a difference output. ! EFFECT: high efficiency of generating a remainder on a given modulo for a stream of numbers by piping the process of calculating partial and resultant remainders based on precalculation of values of primary remainders. ! 2 dwg, 1 tbl, 2 cl