Divisibilidade, números primos e suas aplicações

Abstract

This thesis explores the concepts of divisibility and prime numbers, tracing their origins from ancient Mathematics to modern applications. Divisibility, a fundamental aspect of number theory, was addressed by ancient civilizations and formalized by mathematicians such as Euclid and Gauss. The Fundamental Theorem of Arithmetic, which states the unique factorization of integers into prime factors, is crucial for understanding divisibility. Euclid’s algorithm for computing the Greatest Common Divisor (GCD) is discussed, highlighting its historical importance and its applications in cryptography, particularly in the RSA system where prime numbers are essential for information security. According to the Base National Common Curriculum (BNCC), the study of divisibility and prime numbers is integrated into fundamental education, with proposed practical activities for engaging students. The thesis concludes with reflections on the ongoing relevance of these concepts in Mathematics and technology and suggests future educational projects to deepen classroom knowledge.