Greatest common factor

Learning Objectives Define factors, common factors, and the Greatest Common Factor (GCF). Identify prime and composite numbers. Find the GCF of two numbers by listing all their factors. Find the GCF of two or more numbers using prime factorization. Apply the concept of GCF to solve real-world problems. Explain the steps involved in finding the GCF using different methods. Have you ever needed to share items equally among friends or arrange things into the largest possible equal groups? 🤔 That's where the Greatest Common Factor comes in handy! In this lesson, you'll discover what factors are, how to find common factors between numbers, and most importantly, how to identify the Greatest Common Factor (GCF). Understanding GCF is a fundamental skill in number theory...

TermDefinitionExample FactorA factor of a number is a whole number that divides into that number exactly, without leaving a remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 evenly. Common FactorA common factor is a factor that two or more numbers share.For the numbers 12 and 18, the factors of 12 are {1, 2, 3, 4, 6, 12} and the factors of 18 are {1, 2, 3, 6, 9, 18}. The common factors are 1, 2, 3, and 6. Greatest Common Factor (GCF)The Greatest Common Factor (GCF) is the largest number that divides exactly into two or more numbers.For the numbers 12 and 18, the common factors are 1, 2, 3, and 6. The greatest among these is 6, so GCF(12, 18) = 6. Prime NumberA prime number is a whole number greater than 1 that has exactly two factors: 1 and its...

Listing Factors Method for GCF 1. List all factors for each number. 2. Identify the factors that are common to all numbers. 3. Select the largest factor from the common factors. This method is effective for finding the GCF of smaller numbers where listing all factors is manageable. It directly shows all possible common factors. Prime Factorization Method for GCF 1. Find the prime factorization of each number. 2. Identify all prime factors that are common to all numbers. 3. For each common prime factor, take the lowest power (or count) it appears in any of the factorizations. 4. Multiply these common prime factors (with their lowest powers) together. This method is generally more efficient for larger numbers or for finding the GCF of three or more numbers. It relies on breaki...