Prime factorization

Learning Objectives Define and identify prime and composite numbers. Explain what a prime factor is. Use a factor tree to find the prime factorization of a composite number. Use the division method to find the prime factorization of a composite number. Write the prime factorization of a number using exponents. Recognize that every composite number has a unique set of prime factors. Apply divisibility rules to aid in prime factorization. Ever wonder what the 'building blocks' of numbers are? 🧱 Just like LEGOs, numbers can be broken down into their simplest, unbreakable parts! In this lesson, we'll explore how to break down any whole number into its unique set of prime number 'ingredients'. This skill, called prime factorization, is a fundamental c...

TermDefinitionExample FactorA factor is a whole number that divides another whole number exactly, with no remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 evenly. Prime NumberA prime number is a whole number greater than 1 that has exactly two factors: 1 and itself.The number 7 is a prime number because its only factors are 1 and 7. Composite NumberA composite number is a whole number greater than 1 that has more than two factors.The number 10 is a composite number because its factors are 1, 2, 5, and 10 (more than two factors). Prime FactorA prime factor is a 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 of 12 are 2 and 3. Prime FactorizationPrime factorization is the pr...

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 which numbers are 'unbreakable' building blocks. Remember, 1 is NOT a prime number. Definition of a Composite Number A whole number $c > 1$ is composite if it has more than two positive factors. This rule helps us identify which numbers CAN be broken down further into prime factors. All whole numbers greater than 1 are either prime or composite. Fundamental Theorem of Arithmetic (Simplified) Every composite number can be expressed as a product of prime numbers in a way that is unique (except for the order of the prime factors). This means that no matter how you start breaking down a composite number, you will always en...