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

SKETCH’S WORLD GCF GAME Help Sketch stay away from the eraser by finding the GCF http://www.fun4thebrain.com/beyondfacts/gcfsketch.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? 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? 37 prime 51 composite

Prime or Composite? Prime Composite Both Neither 89

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

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

Prime Factorization of 60 & 96

Find the GCF of 42 and 60. = 2 •  3 • 7 60 = 2 • 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/fractions/GreatestCommonFactor.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) 10 and 50 b) 40 and 95 c) 18 and 63 d) 32 and 92

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

Finding GCF: Extra practice (if needed) http://www.mathopolis.com/questions/q.php?id=920&site=1&ref=/greatest-common-factor.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 45a2b3 45A2b3 = 9 • 5 • a • a • b • b • b = 3 • 3 • 5 • a • a • b • b • b Write the variables without exponents.

10cd2 2*5*c*d*d 5*5*c*c*c*d*d GCF Monomials 25c3d2 http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying%20monomials/v/monomial-greatest-common-factor

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 • b 48ab4 = 2 • 2 • 2 • 2 • 3 • a • b • b • b • b What do they have in common? Multiply the factors together. GCF = 8ab

You Try…. Find the GCF of 8a2b and 18a2b2c The GCF is 2a2b

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 10x2y3 and 15xy2

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 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??

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/AV6/Lfaccom.htm

Factoring a Monomial from a polynomial Factor 12x2 - 9x Think…what is the GCF???? 3x is the GCF The GCF always goes on the outside of the parenthesis. The “leftovers” go in the parenthesis Answer: 3x(4x - 3)

Factoring a Monomial from a Polynomial Factor 15x2y3 + 10xy2 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 4x + 4y 4x – 4y 6x – 18y 4a + 36b 4ab + 10bc 4( x + y) 4( x - y) 6( x - 3y) 4( a + 9b) 2b( 2a + 5c)

Quick Check: GCF Binomials 3x2 + 9x 16x + 48x2 10x - 8x2 12a2b + 32ab 25a2t + 100at2 3x( x + 3) 16x( 1 +3x) 2x( 5 – 4x) 4ab(3a + 8 25at(a + 4t)

CLASS WORK Complete the Factoring Binomials worksheet

Practice with Factoring http://regentsprep.org/Regents/math/ALGEBRA/AV6/PracFact4.htm

Factoring a Monomial from a polynomial Factor 9x4 + 18x3 + 6x2 Think…what is the GCF???? 3x2 is the GCF Answer: 3x2 (3x2 + 6x + 2)

Factoring GCF & Trinomials http://www.themathlab.com/Algebra/factoring/grtmono1.htm#answers

GCF Trinomials

GCF QUIZ http://www.softschools.com/quizzes/algebra/finding_the_greatest_common_factor_gcf_of_two_or_more_monomials/quiz5018.html