Transcript Lesson 4-4a
4-4 6th grade math Greatest Common Factor GCF Objective • To find the greatest common factor of two or three numbers • Why? To help you find the fastest and easiest way to simplify fractions. To find the greatest number of items that could be separated into groups. California State Standards NS 2.4 : Determine the … greatest common divisor of whole numbers; use them to solve problems with fractions … MR 2.4: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models to explain mathematical reasoning. Vocabulary • Greatest Common Factor (GCF) – The greatest number that is a factor of each of two or more numbers – How you can MAKE (or factor like a factory makes things) that number using multiplication • 24: 1, 24, 2, 12, 3, 8, 4, 6 How to Find the GCF Separate 12 photos of Boston and 30 photos of Philly into an album with same amount of photos on each page. Use GCF of 12 and 30 1) Start listing the factors of the LOWEST NUMBER first. Start with 1 x ___. Then move on. 2) List all factors, normally stopping at 12 or 13? 3) To find GCF, look at list. Start with the Greatest factor. Ask: can this be a factor to the other number? If yes, that number is the GCF. If no, move on to the next greatest number. Repeat question. Move on if no. If none of the factors work the only factor is 1. 12 = 1, 12, 2, 6, 3, 4 30 = 12 = 1, 12, 2, 6, 3, 4 30 = GCF = 6 pictures per page You should start factoring the smaller number because you will have to less work! Another Way to Factor 48 48 = 12 6x2 Try this other way to find GCF. Try this way if you like to do factor trees or factor ladders. 1. Find the prime factorization of the smaller number. 2. Then find the common prime factors 3. And multiply 4 3x2x2 2x2 60 = 60 6 10 3x2 5x2 PF of 48 = 2 x 2 x 2 x 2 x 3 PF of 60 = 2 x 5 x 2 x 3 Common Factors = 3 x 2 x 2 = GCF = 12 Try It! Find the GCF 1) 6, 15 1) 6 2 GCF 6 and 15 = 3 2) 2) 21, 49 3 21 3 7 GCF 21 and 49 = 7 3) 300, 144 3) 2 144 2 72 2 36 2 18 2 9 3 3 300 2 150 2 75 5 15 3 5 Common Factors= 2 · 2 · 3 = 12 4) 4) 16, 70, 78 16 2 8 2 4 2 2 70 2 35 5 7 78 2 39 3 13 PF 16 = 2, 2, 2, 2 PF 70 = 2, 5, 7 PF 78 = 2, 3, 13 GCF = 2 Objective Review • To find the greatest common factor of two or three numbers. Why? You can now find the fastest and easiest way to simplify fractions. You can find the greatest number of items that could be separated into groups. Independent Practice • Complete problems 6-13. • For a challenge, complete problems 14-16 • Copy original problem first. • Show all work! • If time, complete Mixed Review: 17-22 • If still more time, work on Accelerated Math.