Greatest common factor

Learning Objectives Define factors, common factors, and the Greatest Common Factor (GCF). List all factors of a given whole number. Identify common factors between two or more whole numbers. Determine the GCF of two or more whole numbers using the listing factors method. Determine the GCF of two or more whole numbers using the prime factorization method. Apply the concept of GCF to solve real-world problems. Imagine you have 12 cookies and 18 brownies. How can you arrange them into identical groups with no leftovers? 🤔 This is where the Greatest Common Factor comes in handy! In this lesson, you'll learn what the Greatest Common Factor (GCF) is and discover powerful methods to find it for any set of numbers. Understanding GCF is a fundamental skill in number theory tha...

TermDefinitionExample FactorA factor of a number is a whole number that divides into it exactly, with no 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 of two or more numbers is a number that is a factor of all of them.For 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, 6}. Greatest Common Factor (GCF)The Greatest Common Factor (GCF) of two or more numbers is the largest number that is a factor of all of them.For 12 and 18, the common factors are {1, 2, 3, 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 distinct factors: 1 and itself.5...

Method 1: Listing Factors To find the GCF of two or more numbers, list all factors for each number, identify the common factors, and then select the largest one. This method is effective for smaller numbers where listing factors is manageable. It directly shows all common factors before identifying the greatest. Method 2: Prime Factorization To find the GCF of two or more numbers, first find the prime factorization of each number. Then, multiply all the common prime factors, taking the lowest power (exponent) of each common prime factor. This method is generally more efficient for larger numbers or when dealing with three or more numbers. It relies on breaking numbers down into their fundamental prime components.