Prime factorization with exponents

Learning Objectives Identify prime and composite numbers. Find the prime factors of a composite number using a factor tree. Understand what an exponent represents in mathematical notation. Write repeated prime factors using exponents. Express any composite number as a product of its prime factors using exponents. Explain why prime factorization is unique for every number. Check their prime factorization by multiplying the factors. Ever wonder what secret building blocks make up every number? 🧱 Let's discover how to break numbers down to their simplest, 'prime' ingredients! In this lesson, you'll learn how to find the special prime numbers that multiply together to make any number. We'll also learn a super-short way to write these prime factors us...

TermDefinitionExample Prime NumberA whole number greater than 1 that has exactly two factors: 1 and itself. Think of them as the 'building blocks' of all other numbers.2, 3, 5, 7, 11 are prime numbers. 7 is prime because its only factors are 1 and 7. Composite NumberA whole number greater than 1 that has more than two factors. These numbers can be 'built' from prime numbers.4, 6, 8, 9, 10 are composite numbers. 6 is composite because its factors are 1, 2, 3, and 6. FactorA number that divides another number evenly, with no remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12. Prime FactorA factor of a number that is also a prime number.For the number 12, the factors are 1, 2, 3, 4, 6, 12. The prime factors are 2 and 3. Prime FactorizationWriting a composite number as...

Prime Number Definition A whole number $p > 1$ is prime if its only factors are $1$ and $p$. This rule helps us identify the fundamental building blocks for prime factorization. Numbers like 2, 3, 5, 7 are prime. Composite Number Definition A whole number $c > 1$ is composite if it has more than two factors. This rule helps us identify numbers that can be broken down further into prime factors. Numbers like 4, 6, 8, 9 are composite. Fundamental Theorem of Arithmetic (Simplified) Every composite number can be expressed as a unique product of prime numbers. This means that no matter how you start factoring a number, you will always end up with the same set of prime factors. For example, $12 = 2 \times 2 \times 3$ is the only prime factorization for 12. Expone...