# Greatest Common Factor LESSON ESSENTIAL QUESTION WHAT IS

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Greatest Common Factor LESSON ESSENTIAL QUESTION WHAT IS A GREATEST COMMON FACTOR (GCF)? HOW DO YOU USE GCF TO FACTOR FUNCTIONS?

JOURNAL �Explain how to reduce the fraction 9/12. �Don’t just do it, explain in words HOW to do reduce a fraction.

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 fractions �We are going to take our knowledge of GCF to another level today

What is a factor? �Factors are the numbers you multiply together to get another number �List all the factors of 12 1, 12, 2, 6, 3, 4 �List all the factors of 16 1, 16, 2, 8, 4

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?

GCF of 12 and 16 �Step 1: Find all the factors of each number �Step 2: Circle the common factors �Step 3: Choose the greatest number circled of the common factors �Factors of 12: 1, 12, 2, 6, 3, 4 �Factors of 16: 1, 16, 2, 8, 4 4 is the Greatest Common Factor (GCF)

What is the GCF of 60 & 96? Factors of 60 1 2 3 4 5 6 60 30 20 15 12 10 Factors of 96 1 2 3 4 6 8 96 48 32 24 16 12

SKETCH’S WORLD GCF GAME Help Sketch stay away from the eraser by finding the GCF �http: //www. fun 4 thebrain. com/beyondfacts/gcfsketc h. html

2 ways to GCF �There are 2 ways to finding the Greatest Common Factor…. . We have explored one of the ways! 1. Listing all factors and picking the largest one 2. Prime factorization Now, we need to discuss what a “prime” number is…. .

What is a prime number? 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? 37 prime 51 composite

Prime or Composite? 1. 2. 3. 4. Prime Composite Both Neither 89

Find the prime factorization of 84. 84 = 4 • 21 = 2 • 3 • 7

What is the prime factorization of 48? 1. 3 16 2. 3 4 4 3. 2 2 3 4 4. 2 2 3

Prime Factorization of 60 & 96 Factorization of 60 Factorization of 96

Find the GCF of 42 and 60. 42 = 60 = 2 • 3 • 7 2 • 3 • 5 What 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!

You choose: Find the GCF of 24 & 48

Fruit Shoot Game �Find the Greatest Common Factor game �http: //www. sheppardsoftware. com/mathgames/frac tions/Greatest. Common. Factor. htm

JOURNAL: Let’s practice some more �Choose a method and find the GCF of the following pairs of numbers: �Check your answer with your shoulder buddy. a) b) c) d) 10 and 50 40 and 95 18 and 63 32 and 92

What is the GCF of 48 and 64? 1. 2 2. 4 3. 8 4. 16

Finding GCF: Extra practice (if needed) �http: //www. mathopolis. com/questions/q. php? id=9 20&site=1&ref=/greatest-commonfactor. html&qs=920_921_1382_1383_3548_3549_ 3550_3551

What do you think…. How do you find the GCF of variables? !? !

Find the prime factorization of 45 a 2 b 3 45 A 2 B 3 = 9 • 5 • A • B • B = 3 • 5 • A • B • B WRITE THE VARIABLES WITHOUT EXPONENTS.

GCF Monomials 2 10 cd 25 c 3 d 2 2*5*c*d*d 5*5*c*c*c*d*d http: //www. khanacademy. org/math/algebra/multiplying-factoringexpression/multiplying%20 monomials/v/monomial-greatest-common-factor

Find the GCF of 40 a 2 b and 48 ab 4. 40 a 2 b = 2 • 2 • 5 • a • b 48 ab 4 = 2 • 2 • 3 • a • b • b What do they have in common? Multiply the factors together. GCF = 8 ab

You Try…. �Find the GCF of 8 a 2 b and 18 a 2 b 2 c The GCF is 2 a 2 b

HOMEWORK �COMPLETE THE GCF WORKSHEET FOR HOMEWORK TONIGHT

Factoring a Monomial from a polynomial LESSON ESSENTIAL QUESTION: HOW DO YOU USE GCF TO FACTOR POLYNOMIALS?

JOURNAL: WARMUP �Find the GCF of 10 x 2 y 3 and 15 xy 2

What more can we do with GCF? �Now, that we have mastered how to GCF monomials…… �We are going to GCF polynomials

�We have seen that we use multiplication to get 4 x 2(2 x + 1) = 8 x 3 + 4 x 2 �What if we start with 8 x 3 + 4 x 2 and want to get to 4 x 2(2 x + 1) ? �How do we do that? ?

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

Finding Common Factors �http: //regentsprep. org/Regents/math/ALGEBRA/A V 6/Lfaccom. htm

Factoring a Monomial from a polynomial Factor 12 x 2 - 9 x Think…what is the GCF? ? 3 x is the GCF The GCF always goes on the outside of the parenthesis. The “leftovers” go in the parenthesis Answer: 3 x(4 x - 3)

Factoring a Monomial from a Polynomial Factor 15 x 2 y 3 + 10 xy 2 The 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: ________

Quick Check: GCF Binomials 4 x + 4 y 4 x – 4 y 6 x – 18 y 4 a + 36 b 4 ab + 10 bc 4( x + y) 4( x - y) 6( x - 3 y) 4( a + 9 b) 2 b( 2 a + 5 c)

Quick Check: GCF Binomials 3 x 2 + 9 x 16 x + 48 x 2 10 x - 8 x 2 12 a 2 b + 32 ab 25 a 2 t + 100 at 2 3 x( x + 3) 16 x( 1 +3 x) 2 x( 5 – 4 x) 4 ab(3 a + 8 25 at(a + 4 t)

CLASS WORK �Complete the Factoring Binomials worksheet

Practice with Factoring �http: //regentsprep. org/Regents/math/ALGEBRA/A V 6/Prac. Fact 4. htm

Factoring a Monomial from a polynomial Factor 9 x 4 + 18 x 3 + 6 x 2 Think…what is the GCF? ? 3 x 2 is the GCF Answer: 3 x 2 (3 x 2 + 6 x + 2)

Factoring GCF & Trinomials �http: //www. themathlab. com/Algebra/factoring/grt mono 1. htm#answers

GCF Trinomials

GCF QUIZ �http: //www. softschools. com/quizzes/algebra/findin g_the_greatest_common_factor_gcf_of_two_or_m ore_monomials/quiz 5018. html