Article's purpose. The purpose of this article is to determine the number-theoretical component in the structure of the Math teacher’s mathematical competence, to fill its contents for a consistent readiness to carry out professional activities. Methodology. The presented work mainly included theoretical research methods (system analysis of the structure of the Math teacher’s professional competence, a comparative analysis of the contents of education and a complex of modern mathematics, theoretical modeling of learning process sequence) as well as expert assessment of the importance of mastering number theory issues by Math teachers working in different conditions. Scientific novelty. Based on the hierarchical structure of mathematical competence, we determine the place of the number-theoretical component and its coherence with other components of mathematical competence. It is theoretically substantiated that the level of the number-theoretical component of the Math teacher’s mathematical competence significantly affects the effectiveness of the teacher’s professional activity. A flexible model of the number-theoretical component of mathematical competence and a recurкуте method of forming its levels are proposed. The flexibility of the model provides for the possibility of various degrees of skills at each level. The requirements for a holistic system of teacher skills relating to the theory of numbers are formed and substantiated. For this reason we introduced the concept of logical-didactic mathematical theory which contains formal inference rules as well as heuristic strategies for constructing chains of so-called expedient problems by contrast with formal mathematical theory. A high degree of skills at appropriate levels allows the teacher to effectively generate such chains. Conclusions. The practical use of this research may be relevant while forming courses programs in algebra and theory of numbers, the methodology of teaching mathematics, elementary mathematics in pedagogical and classical universities, as well as forming the contents of teacher advanced training courses in postgraduate teacher education. The issues of measuring the levels of the number-theoretical component of the Math teacher’s mathematical competence, conducting experiments to test the effectiveness of the Math teacher’s activities depending on it, building a concept for developing number-theoretical component of the Math teacher’s mathematical competence while continuing education are the tasks of further research.