Prime and composite numbers

Learning Objectives Define prime and composite numbers. Distinguish between prime and composite numbers for any given natural number greater than 1. Identify all factors of a given natural number. Explain why the number 1 is neither prime nor composite. Apply divisibility rules to efficiently determine factors of a number. Perform prime factorization for composite numbers. Understand the unique prime factorization of any composite number. Have you ever wondered what makes some numbers 'special' and others not? 🤔 Let's uncover the secret building blocks that make up all other whole numbers! In this lesson, you will learn about prime and composite numbers, which are fundamental concepts in mathematics. Understanding these numbers will help you simplify fract...

TermDefinitionExample Natural NumbersThe counting numbers: 1, 2, 3, 4, and so on. Also known as positive integers.The numbers 7, 25, and 100 are all natural numbers. FactorA number that divides another number exactly, leaving no remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 evenly. Prime NumberA natural number greater than 1 that has exactly two distinct positive factors: 1 and itself.The number 7 is a prime number because its only factors are 1 and 7. Composite NumberA natural number greater than 1 that has more than two distinct positive factors.The number 10 is a composite number because its factors are 1, 2, 5, and 10 (more than two factors). DivisibilityThe ability of one number to be divided by another number without a remainder.20 is...

Definition of a Prime Number A natural number $p > 1$ is prime if its only positive factors are 1 and $p$. To check if a number is prime, find all its factors. If it only has two factors (1 and itself), it's prime. For example, 5 is prime because its factors are 1 and 5. Definition of a Composite Number A natural number $c > 1$ is composite if it has more than two positive factors. To check if a number is composite, find all its factors. If it has more than two factors, it's composite. For example, 6 is composite because its factors are 1, 2, 3, and 6. The Special Case of Number 1 The number 1 is neither prime nor composite. The definitions of prime and composite numbers both state 'greater than 1'. The number 1 only has one factor (itself),...