The paper discusses adaptive filtering using Least Mean Square (LMS) and Recursive Least Square (RLS) algorithms. An algorithm for adjusting the coefficients of an adaptive digital filter in the Residue Number System and a procedure of developed algorithm applying depending on filter length and signal length are proposed. Mathematical modeling of the considered algorithms is performed. Examples are presented to demonstrate how the proposed technique can help the designer in the adjustment of the filter coefficients without the need for extensive trial-and-error procedures. The analysis of the denoising quality and computational complexity is made. Synthetic and real data (earthquake recording) were used while testing. The proposed algorithm surpasses the existing ones like LMS and RLS, and their modifications in a number of parameters: adaptation (denoising) quality, ease of implementation, execution time. The main difference between the developed algorithm is the sequential adaptation of each coefficient with zero error. In the known algorithms, the entire vector of coefficients is iteratively adapted, with some specified accuracy. The iterations (steps) number is determined by the input signal length for all algorithms.