Currently, the solution of Olympiad tasks is of great importance in schools. The main goal here is to teach the student to use his mathematical abilities in his environment, as well as to develop his intellectual abilities. As the mathematician K. Gauss said: "Mathematics is the king of sciences," he says, "number theory is the king of mathematics." In this regard, the divisibility of integers is considered one of the important topics in mathematics Olympiads in the number theory section. "The topic of divisibility of integers" is one of the most frequently encountered, important topics at mathematical Olympiads.
Of great importance for students participating in the Olympiad is independent reading, understanding the task through examples of tasks. At any time, the teacher may not give students feedback, and in such cases, methodological manuals, sets with sample assignments are an indispensable tool for students. This article provides methods for solving problems of dividing integers with remainder, without remainder, specific examples with a complete solution model. In order for students to understand the task, tasks for independent work of the student are given as consolidation of the acquired knowledge. The tasks were compiled by class, depending on the complexity, the level of understanding of the students.