Chapter 1
Numbers and Operations
Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Numbers And Operations
1. Uses the definitions of prime and composite numbers to solve problems
Prime numbers are natural numbers greater than 1 that have exactly two distinct factors: 1 and the number itself. The sequence begins 2, 3, 5, 7, 11, 13, 17, 19, 23, … . The number 2 is the only even prime because every even number larger than 2 has at least three factors (1, 2, and itself).
Composite numbers are integers greater than 1 that have more than two factors. For example, 20 is composite because it can be expressed as 1 × 20, 2 × 10, and 4 × 5.
The identification of prime and composite numbers is the foundation for prime factorization, which expresses any composite number as a product of primes. For instance, 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7. This decomposition is unique for every integer greater than 1, a principle known as the Fundamental Theorem of Arithmetic.