Prime factorization

Learning Objectives Define prime and composite numbers. Identify the factors of a given number. Explain what prime factorization means. Use factor trees to find the prime factorization of a number. Use the division method to find the prime factorization of a number. Write the prime factorization using exponents. Understand the uniqueness of a number's prime factorization. Ever wonder what the 'building blocks' of numbers are? 🧱 Let's break numbers down to their simplest, most fundamental parts! In this lesson, you'll learn how to find the prime factors of any number. This skill helps us understand numbers better, simplify complex problems, and is a fundamental concept in many areas of mathematics. Real-World Applications Simplifying fractions...

TermDefinitionExample 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 whole number greater than 1 that has exactly two factors: 1 and itself.2, 3, 5, 7, 11 are prime numbers. For example, the only factors of 7 are 1 and 7. Composite NumberA whole number greater than 1 that has more than two factors (meaning it can be divided evenly by numbers other than 1 and itself).4, 6, 8, 9, 10 are composite numbers. For example, the factors of 6 are 1, 2, 3, and 6. Prime FactorA factor of a number that is also a prime number.For the number 12, its factors are 1, 2, 3, 4, 6, 12. The prime factors are 2 and 3. Prime FactorizationThe process of expressing a composite numbe...

Definition of a Prime Number A whole number $p > 1$ is prime if its only positive factors are $1$ and $p$. This rule helps us identify the fundamental 'building blocks' (prime numbers) that we use in prime factorization. Numbers like 2, 3, 5, 7, 11, etc., fit this rule. Definition of a Composite Number A whole number $c > 1$ is composite if it has more than two positive factors. This rule tells us which numbers can be broken down further into smaller factors, eventually leading to their prime factors. Numbers like 4, 6, 8, 9, 10, etc., fit this rule. Fundamental Theorem of Arithmetic (Simplified) Every composite number can be written as a unique product of prime numbers, regardless of the order of the factors. This rule guarantees that no matter which...