Finding the Greatest Common Factor Looking Inside the Number Values

What Is Our Objective???? We will find the greatest common factor of a set of numbers. We will look at word problems that use greatest common factors as a solution. Using primes will be emphasized in this lesson. You will see a type of problem for which prime factors are the only solution!!

The first method students learn when finding GCF is the “list and look” method. This works just fine when values are similar to: 16 = 24 = 1, 16, 2, 8, 4, 4 1, 24, 2, 12, 3, 8, 4, GCF = 8 We will use a new method to prepare for more difficult problems. 90= 45= 60= We will use the think boxes we used last week. We will also organize our primes into “swim lanes.” 9 ∙10 9 ∙5 10 ∙ Each factor has its own “lane.” 3 3 5Line up “shared” factors You had to create a new lane for the other 2. Multiply the factors shared by ALL values. 3 x 5 = 15, so 15 is the GCF

Why learn a new way??? In future classes, you will have values similar to this: 24ab 2 18abc Using primes will help with the GCF for these terms, called monomials. 4 x 6 x a x b x b 3 x 6 x a x b x c a b b a b c 6ab is the GCF.

Word Problem Application There are 12 boys and 18 girls in science class. What is the most even distribution of boys and girls when the class is broken into lab groups? 12= boys 18= girls Just like the methods for finding prime factorization, different methods work best in different situations. The list method works best here. 6 X 2 6 X 3 The best arrangement for the lab groups is 6 groups. Each group will have 2 boys and 3 girls in it. 12 = 1, 12 2, 6 3, 4 18 = 1, 18 2, 9 3, 6 0 0

Practice, practice, practice 18= 27= 32= 72= 21= 42= 56= 9 ∙ 2 9 ∙ ∙ 4 8 ∙ ∙ 6 7 ∙ 8 7 ∙ GCF = 9 GCF = 8 GCF = 7

15 = 28= 77= 5∙3 4∙7 7∙ ________________7 11 GCF=1 Many of you liked the division ladder. This will work too! x 2 x 2 x 2 x x 2 x 2 x x 2 x 2 x 7 GCF=8

Word Problem Kim has 16 red roses and 20 pink roses. What arrangement would evenly distribute the flowers? 16= 4 x 4 20 = 4 x 5 There would be 4 arrangements. Each would have 4 red roses and 5 pink roses. 16 = 1, 16 2, = 1, 20 2, 10 4, 5

What Have We Accomplished? We used two methods to find the greatest common factor of a set of numbers We used the greatest common factor to find the solution to word problems