Abstract
The article is devoted to the divisors of natural numbers and properties related to the factorization of a natural number. In particular, the article deals with the canonical form of writing the decomposition of a number into prime factors, its generalization in the form of an infinite multiplicative structure, and the number of divisors of a given number. In addition, the concepts of chains of divisors of a number, factors of chains of divisors, mutual conditioning of a chain of divisors and sequences of its factors are considered. The so-called dense chains of divisors of a given number are separately investigated and how the lengths of such chains are related to its multiplicative structure, two methods of counting the total number of dense chains of divisors of a given number are given. The article is addressed to schoolchildren, teachers of general secondary education institutions and everyone who loves mathematics.
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