SUMMARY
Context. Ensuring high-speed calculation by computer systems of the classical task of factorization of integer value on simple factorsrequires the development of effective algorithmic methods using the latest information technologies. Fast computation of factorization ofnumbers to provide high cryptocapability of information data, using multidimensional representation of one-dimensional sequences ofinformation data and other applications is sufficiently in demand in many practical tasks.Objective.The purpose of the work is to improve the method of trial divisions to compute the factorization of integer value with usingparallelization of computations and efficient use of computing resources of computer systems, which ensures faster computation of thevalues of prime factors of the decomposition.Method. It is proposed to use the residuals of each digit of the binary representation of the factorization number in order to check fordivisibility in the method performing of trial divisions into prime numbers.Results. The result of the study is to develop of a program of parallel execution of the factorization of integer value in computer systemswith multi-core processors.Conclusions. In the research, a method of checking for divisibility using the residuals of each digit of the binary representation of thefactorization number was applied, which allows for multi-threaded mode to execute the decomposition of the number into the factors. Thebasic idea of applying the corresponding mathematical apparatus is to use the residuals of the integer exponent of the number two from primenumbers. As a result, the accumulation of residuals is performed, which is checked for equality with the corresponding prime number and itsdegrees. The possibility of a multithreaded software organization for computing the number factorization ensures its parallel execution inmulti-core processors of computer systems