Prime factorization

Learning Objectives Define prime and composite numbers. Identify prime numbers up to 100. Explain the concept of prime factorization. Use factor trees 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 exponential notation. Ever wondered how numbers are built from their most basic 'ingredients'? 🤔 Just like molecules are made of atoms, numbers are made of primes! In this lesson, you'll discover how to break down any composite number into its unique set of prime building blocks. Understanding prime factorization is a fundamental skill in number theory and will help you simplify fractions, find common multiples, and even understand...

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 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. Other examples include 2, 3, 5, 11, 13. Composite NumberA composite number is a natural number greater than 1 that has more than two distinct positive factors (i.e., it is not prime).The number 10 is a composite number because its factors are 1, 2, 5, and 10. Other examples include 4, 6, 8, 9, 12. Prime FactorA prime factor is a factor of a number that is also a prime number.For the number 12, i...

Fundamental Theorem of Arithmetic Every integer greater than 1 is either a prime number itself or can be represented as a product of prime numbers, and this representation is unique, up to the order of the factors. This rule tells us that prime numbers are the 'building blocks' of all other whole numbers, and there's only one way to build each number from primes (if we ignore the order). Prime Factorization using Exponents When writing the prime factorization of a number, if a prime factor appears multiple times, you can use exponents to simplify the notation: $N = p_1^{a_1} \times p_2^{a_2} \times \dots \times p_k^{a_k}$ This rule provides a concise way to write prime factorizations. For example, instead of $2 \times 2 \times 2 \times 3$, we write $2^3 \times...