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4.2 Greatest Common Factor ( ) Math 7 Vocabulary *** Common Factor: a whole number that is a factor of 2 or more nonzero whole numbers. ***Greatest Common Factor (GCF): the greatest of the common factors ***Relatively Prime: two or more nonzero whole numbers whose GCF is 1. Examples ** Ex. 1: Finding the Greatest Common Factor 3 methods Strategy 1: To find the GCF, list all the factors of each number. The largest factor that is in both numbers is the GCF. Strategy 2: To find the GCF, write the prime factorization of each number and identify which factors are in each number. Strategy 3: Upside down division: 2 /60 96 2 /30 48 3 /15 24 5 8 Try these on your own: Find the GCF using any method 1. 16, 28 2. 15, 75, 20 3. What is the greatest number of ensembles that can be formed with 32 violinists, 40 violists, and 16 cellists? How many of each instrument will be in each ensemble? ** Ex. 2: Identifying Relatively Prime Numbers Try these on your own: Tell whether the numbers are relatively prime. 1. 13, 24 2. 16, 25 Guided Practice/Ticket out the Door