Master Number Theory Fundamentals

Explore the building blocks of mathematics from a developer's perspective. Learn how these concepts power modern cryptography, algorithms, and data structures.

🔍 Try Examples ✍️ Practice Problems

Key Concepts

Prime Numbers

Números primos são números naturais maiores que 1 que têm divisores exclusivamente 1 e ele mesmo. Eles são as partes essenciais da teoria dos números.

Divisibility

Entender divisibilidade nos permite determinar se um número é divisível por outro, formando a base para algoritmos de otimização em ciência da computação.

Prime Factorization Demo

Input Number:

Examples:

  • 24 ➝ 2×2×2×3
  • 884 ➝ 2×2×13×17
  • 1111 ➝ 11×101
Resultado aparecerá aqui (ex: 48 = 2 × 2 × 2 × 2 × 3)

Foundational Concepts

The following sections cover the fundamental mathematical principles that all developers should understand for algorithm design and system optimization.

1

Greatest Common Divisor (GCD)

The Largest number that divides both numbers without remainder

JavaScript Implementation

function gcd(a, b) {
    return b === 0 ? a : gcd(b, a % b);
}

// Example usage:
let result = gcd(48, 18); // Returns 6

Mathematical Representation

GCD(a, b) = max{d ∈ ℕ | d|a ∧ d|b}

Where "d|a" means d divides a without remainder

2

Modular Arithmetic

Essencial para criptografia e programação com números grandes.

Current value: ...

Modulo base: 12

Try It Out!

Practice Problems

Test your understanding with these interactive challenges. Solutions are provided with step-by-step explanations.

Problem 1: Prime Identification

Determine whether the following numbers are prime or composite. Show your work using trial division method.

Problem 2: GCD & LCM

Compute GCD and LCM for 432 and 528 using prime factorization method.