The main objective of factor analysis is to identify implicit factors that explain the relationships between observed variables. This makes it possible to obtain a more complete and accurate picture of the phenomena and processes being studied, which allows us to establish hidden patterns and trends that are not always possible to determine with visual data analysis. These hidden variables can be used to simplify the data and understand the main mechanisms underlying the phenomenon being studied.A quantitative assessment of the influence of each variable on the result using mathematical methods can be performed using various approaches and tools. A brief overview of the main tools is given. The choice of a specific method depends on the nature of the data, the objectives of the study and the available resources.It is known that the main disadvantage of factor analysis is the failure to fulfill the commutative (communicative) law of multiplication, which is explained by the occurrence of an indecomposable remainder. The indecomposable remainder is explained by the fact that the model under consideration does not fully take into account all the factors influencing the phenomenon under study, and therefore the variation of the feature will not be determined only by the factors under consideration, that is, some part will remain undistributed between the independent variables. Consequently, the degree of influence of a specific feature on the dynamics of the resulting component will depend on its location in the model. It is clear that with an increase in the model dimension, the number of equivalent calculation options will also increase due to an increase in the number of possible alternative versions of the solution. It should be noted that this leads to a variety of possible forms of solving the original problem, and the definition of a specific solution method will be determined by the purpose and objectives of the study. It should be noted that the number of options for the possible permutations of factors under consideration can be reduced by aggregating some factors. It is only important to clearly justify the economic meaning of such an aggregated indicator. This circumstance makes it possible to construct a procedure that allows estimating the indecomposable remainder. The article discusses a methodology for estimating the indecomposable remainder. The value of the indecomposable remainder can be defined as the difference between the data obtained in two calculation forms, between the values of the indicator in the multiplicative model, where this indicator is in last place, and in another calculation method, where the same factor is put in first place. It is shown that in the course of factor analysis there is an invariant constant that does not depend on the calculation method. Methods for reducing the dimensionality of the original problem by aggregating the original factors are also given. It is only important to clearly substantiate the economic meaning of such an aggregated indicator. The article provides an example of a three-factor model of labor productivity, when the result indicator will be determined by three factors: capital productivity, mechanical equipment of workers and the share of workers in the total number of employees of the enterprise. By combining the first two factors into one, the problem was reduced to a two-factor model of labor productivity, depending on two factors: the average output of workers and the share of workers in the total number of employees of the enterprise.

factor analysis, multiplicative model, chain substitution method, index method, unresolved remainder, two-factor model, multifactor model, factor aggregation, rule of the index method of factor analysis, invariant constant.