Page 1: Number Decomposition and Prime Factorization
This page introduces fundamental concepts of number theory and prime factorization. The content focuses on breaking down numbers into their prime factors and finding divisors.
Definition: Prime factorization is the process of decomposing a number into a product of its prime factors.
Example: The number 504 is decomposed as follows:
504 = 2 × 252
504 = 2 × 2 × 126
504 = 2 × 2 × 2 × 63
504 = 2³ × 7 × 3²
Highlight: When finding divisors of a number, systematic decomposition helps identify all possible factors. For instance, 198 has divisors: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198.
Vocabulary: Euclidean division involves a dividend, divisor, quotient, and remainder, where the remainder must be less than the divisor.