LESSON ESSENTIAL QUESTION WHAT IS A GREATEST COMMON FACTOR (GCF)? HOW DO YOU USE GCF TO FACTOR...

LESSON ESSENTIAL QUESTION

WHAT IS A GREATEST COMMON FACTOR (GCF)?

HOW DO YOU USE GCF TO FACTOR FUNCTIONS?

Greatest Common Factor

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?

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, 4List 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)

Factors of 60 Factors of 96

1 602 303 204 155 126 10

1 962 483 324 246 168 12

What is the GCF of 60 & 96?

SKETCH’S WORLD GCF GAME

Help Sketch stay away from the eraser by finding the GCFhttp://

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?

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

prime51

composite

Prime or Composite?

1. Prime2. Composite3. Both4. Neither

89

Find the prime factorization of 84.

84 = 4 • 21= 2 • 2 • 3 • 7

What is the prime factorization of 48?

1. 3 162. 3 4 43. 2 2 3 44. 2 2 2 2

3

Factorization of 60 Factorization of 96

Prime Factorization of 60 & 96

Find the GCF of 42 and 60.

What prime factors do the numbers have in common?Multiply those numbers.

The GCF is 2 • 3 = 66 is the largest number that

can go into 42 and 60!

42 = 2 •  3 • 760 = 2 • 2 • 3 • 5

You choose: Find the GCF of 24 & 48

Fruit Shoot Game

Find the Greatest Common Factor gamehttp://www.sheppardsoftware.com/mathgame

s/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 50b) 40 and 95c) 18 and 63d) 32 and 92

What is the GCF of 48 and 64?

1. 22. 43. 84. 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?!?!

45A2B3 = 9 • 5 • A • A • B • B • B

= 3 • 3 • 5 • A • A • B • B • B

WRITE THE VARIABLES WITHOUT EXPONENTS.

Find the prime factorization of 45a2b3

10cd2 25c3d2

2*5*c*d*d 5*5*c*c*c*d*d

GCF Monomials

http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying%20monomials/v/monomial-greatest-common-factor

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

LESSON ESSENTIAL QUESTION:

HOW DO YOU USE GCF TO FACTOR POLYNOMIALS?

Factoring a Monomial from a polynomial

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 + 4y4x – 4y6x – 18y4a + 36b4ab + 10bc

4( x + y)

4( x - y)

6( x - 3y)

4( a + 9b)

2b( 2a + 5c)

Quick Check: GCF Binomials

3x2 + 9x16x + 48x2

10x - 8x2

12a2b + 32ab25a2t + 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