Factors

Learning Objectives Define and identify factors of a given whole number. Distinguish between prime and composite numbers. Perform prime factorization of composite numbers using various methods. Calculate the Greatest Common Factor (GCF) of two or more numbers. Calculate the Least Common Multiple (LCM) of two or more numbers. Apply factor concepts to solve real-world problems and simplify mathematical expressions. Ever wonder how numbers are built from smaller pieces? 🏗️ What are the fundamental components that make up any whole number? In this lesson, you'll discover the fascinating world of factors, prime numbers, and how to break down numbers into their prime components. Understanding factors is crucial for simplifying fractions, solving algebraic equations, and even...

TermDefinitionExample FactorA factor of a whole number is a number that divides it exactly, leaving no remainder. Factors always come in pairs.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 distinct factors: 1 and itself.The numbers 2, 3, 5, 7, 11, and 13 are prime numbers. For instance, 7 only has factors 1 and 7. Composite NumberA composite number is a whole number greater than 1 that has more than two factors (i.e., it is not prime).The numbers 4, 6, 8, 9, 10, and 12 are composite numbers. For instance, 9 has factors 1, 3, and 9. Prime FactorizationPrime factorization is the process of expressing a composite number as a product of its prime factors. This repres...

Definition of a Factor If $a \times b = c$, where $a$, $b$, and $c$ are whole numbers, then $a$ and $b$ are factors of $c$. This rule defines what a factor is. To find factors, you look for pairs of numbers that multiply to give the original number. Every whole number greater than 1 has at least two factors: 1 and itself. Fundamental Theorem of Arithmetic (Prime Factorization) 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 can be written as $N = p_1^{a_1} \times p_2^{a_2} \times \dots \times p_k^{a_k}$, where $p_i$ are distinct prime numbers and $a_i$ are positive integers. This theorem is the basis for prime factorization. It tells us t...