Presentation on theme: "Greatest Common Factor"— Presentation transcript:
1 Greatest Common Factor Lesson Essential QuestionWhat is a greatest common factor (GCF)?How do you use GCF to factor functions?
2 JOURNAL Explain how to reduce the fraction 9/12. Don’t just do it, explain in words HOW to do reduce a fraction.
3 Reducing a fraction Reduce the fraction 9/12 into simplest form Did you know that since elementary school, you have been using Greatest Common Factors when you reduce fractionsWe are going to take our knowledge of GCF to another level today
4 What is a factor? 1, 12, 2, 6, 3, 4 1, 16, 2, 8, 4 What is a factor? Factors are the numbers you multiply together to get another numberList all the factors of 121, 12, 2, 6, 3, 4List all the factors of 161, 16, 2, 8, 4
5 What is GCF?What is a Greatest Common Factor (GCF)?The highest number that divides exactly into 2 or more numbers.Now that we know what the factors of 12 and 16 are, let’s take a look at the GCF of 12 and 16.What should we be looking for?
6 GCF of 12 and 16 Step 1: Find all the factors of each number Step 2: Circle the common factorsStep 3: Choose the greatest number circled of the common factorsFactors of 12:1, 12, 2, 6, 3, 4Factors of 16:1, 16, 2, 8, 44 is the Greatest Common Factor (GCF)
7 What is the GCF of 60 & 96?Factors of 60Factors of 96
8 SKETCH’S WORLD GCF GAME Help Sketch stay away from the eraser by finding the GCF
9 2 ways to GCFThere are 2 ways to finding the Greatest Common Factor…..We have explored one of the ways!1. Listing all factors and picking the largest one2. Prime factorizationNow, we need to discuss what a “prime” number is…..
10 What is a prime number? composite A prime number is a number that can only be divided by only 1 and itself.A composite number is a number greater than one that is not prime. It has factors.Prime or composite?37prime51composite
15 Find the GCF of 42 and 60.= 2 • • 760 = 2 • 2 • 3 • 5What prime factors do the numbers have in common? Multiply those numbers. The GCF is 2 • 3 = 6 6 is the largest number that can go into 42 and 60!
24 What do they have in common? Multiply the factors together. GCF = 8ab Find the GCF of 40a2b and 48ab4.40a2b = 2 • 2 • 2 • 5 • a • a • b48ab4 = 2 • 2 • 2 • 2 • 3 • a • b • b • b • bWhat do they have in common?Multiply the factors together.GCF = 8ab
25 You Try….Find the GCF of 8a2b and 18a2b2cThe GCF is 2a2b
26 HOMEWORKCOMPLETE THE GCF WORKSHEET FOR HOMEWORK TONIGHT
27 Factoring a Monomial from a polynomial Lesson essential question:How do you use gcf to factor polynomials?
28 JOURNAL: WARMUPFind the GCF of 10x2y3 and 15xy2
29 What more can we do with GCF? Now, that we have mastered how to GCF monomials……We are going to GCF polynomials
30 We have seen that we use multiplication to get 4x2(2x + 1) = 8x3 + 4x2 What if we start with 8x3 + 4x2 and want to get to 4x2(2x + 1) ?How do we do that??
31 Factoring Polynomials Factoring a polynomial means finding an equivalent expression that is a product.Let’s start exploring into bigger polynomials and see what we can figure out
33 Factoring a Monomial from a polynomial Factor 12x2 - 9xThink…what is the GCF????3x is the GCFThe GCF always goes on the outside of the parenthesis. The “leftovers” go in the parenthesisAnswer: 3x(4x - 3)
34 Factoring a Monomial from a Polynomial Factor 15x2y3 + 10xy2The largest integer that will divide into 15 and 10 is _____The largest power of x in both terms is ________The largest power of y in both terms is ________The GCF is _________ Answer:________________
35 Quick Check: GCF Binomials 4x + 4y 4x – 4y 6x – 18y 4a + 36b 4ab + 10bc4( x + y)4( x - y)6( x - 3y)4( a + 9b)2b( 2a + 5c)