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## Prime Factorization

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**http://www.brainpop.com/math/numbersandoperations/factoring/**Brainpop - Factoring video .. Answer the questions**http://www.brainpop.com/math/numbersandoperations/factoring/quiz/**http://www.brainpop.com/math/numbersandoperations/factoring/quiz/ Answers: C D B A A D C B C A**Factor**The numbers that are multiplied to get a product • 15 = 3 x 5 • 3 and 5 are factors of 15 2 x 9 = 18 2 & 9 are factors of 18 3 x 2 =6 3 & 2 are factors of 6**Prime Number**is a counting number that only has two factors, itself and one. • One is not a prime 7 is a prime 5 is a prime**Composite Number**Counting numbers which have more than two factors (such as six, whose factors are 1, 2, 3 and 6) • One is not a composite 8 is a composite 55 is a composite**A Rhyme to Help Us Remember**Prime number Prime number What do you see? I see no other factors Except for one and me. Composite number Composite number What do you see? I see at least three factors Including one and me.**All of the orange numbers on this chart are prime. Write**them down. Refer to them so you don’t waste time trying to factor them.**Prime Factorization**When a composite number is written as a product of all of its prime factors Using the Factor Tree 78 / \ / \ 2 x 39 / / \ / / \ 2 x 3 x 13**Let’s Try a Factor Tree!**84 / \ 2 x 42 / / \ 2 x 2 x 21 / / / \ 2 x 2 3 x 7**72**/ \ 8 x 9 / \ / \ 2 x 4 x 3 x 3 / \ 2 x 2 x 2 x 3 x 3 72 / \ 2 x 36 / / \ 2 x 2 x 18 / / / \ 2 x 2 x 2 x 9 / / / / \ 2 x 2 x 2 x 3 x 3 Factor Trees do not look the same for the same number, but the final answer is the same.**Greatest Common Factor**The largest common factor of 2 or more numbers GCF of 24 and 36 Is 12 Use prime factorization or ladder to find GCF GCF of 72 and 84 Is 12**72**/ \ 8 x 9 / \ / \ 2 x 4 x 3 x 3 / \ 2 x 2 x 2 x 3 x 3 Take the common prime factors of each number and multiply to find the greatest common factor. 84 / \ 2 x 42 / / \ 2 x 2 x 21 / / / \ 2 x 2 3 x 7 2 x 2 x 3 = 12 Prime Factorization is helpful for finding greatest common factors.**Least Common Multiple**The smallest product that both numbers have in common LCM of 5 & 7 Is 35 LCM of 4 & 10 is 20 LCM of 12 & 15 Is 60**72**6 = 84 7 Use the Ladder for LCM, GCF and Simplifying Fractions 2 72 84 WRITEthe two numbers on one line. 2 36 42 DRAW THE L SHAPE 3 18 21 DIVIDEout common prime numbers starting with the smallest 6 7 LCM = 2 2 3 6 7 = 504 LCMmakes an L: GCF = 2 2 3 = 12 GCFis down the left side: Simplified fraction is on the bottom**24**2 = 36 3 Use the Ladder for LCM, GCF and Simplifying Fractions WRITEthe two numbers on one line. 2 24 36 2 12 18 DRAW THE L SHAPE DIVIDEout common prime numbers starting with the smallest 3 6 9 2 3 LCM = 2 2 3 2 3 = 72 LCMmakes an L: GCF = 2 2 3 = 12 GCFis down the left side: Simplified fraction is on the bottom**6**2 = 9 3 Use the Ladder for LCM, GCF and Simplifying Fractions WRITEthe two numbers on one line. 3 6 9 2 3 DRAW THE L SHAPE DIVIDEout common prime numbers starting with the smallest LCM = 3 2 3 = 18 LCMmakes an L: GCF = 3 GCFis down the left side: Simplified fraction is on the bottom**5**5 = 7 7 Use the Ladder for LCM, GCF and Simplifying Fractions WRITEthe two numbers on one line. 5 7 5 7 DRAW THE L SHAPE DIVIDEout common prime numbers starting with the smallest LCM = 5 x 7 = 35 LCMmakes an L: GCF = 1 GCFis down the left side: Simplified fraction is on the bottom**HOMEWORK**• PG 77 4 – 40 evens only 8-16 use ladder 26-32 use factor trees 34-40 use ladder method**Resources**• Brain Pop – Prime Factors • Brain Pop - Prime Numbers • Brain Pop - Exponents**Interactive Practice for Factor Trees**Virtual Manipulatives Interactive Practice 1 Interactive Practice from MathPlayground.com**The Birthday Cake Methoda.k.a. The Box Method**An alternative to factor trees A video from YouTube**Challenge Problem**• Use what you know about multiplying whole numbers by variables and exponents to make a factor tree for the following monomial 45x3 x3 45 9 5 x x x 3 3**A Random Thought about Prime Numbers**Brought to you from YouTube.com**24**2 = 36 3 Use the Ladder for LCM, GCF and Simplifying Fractions WRITE the two numbers on one line. 2 24 36 2 12 18 DRAW THE L SHAPE DIVIDE out common prime numbers starting with the smallest 3 6 9 2 3 LCM = 2 2 3 2 3 = 72 LCM makes an L: GCF = 2 2 3 = 12 GCF is down the left side: Simplified fraction is on the bottom**Ch Test this ThursdayBig Rocks Quiz tomorrow – Decimal**rules #1Four Sight paperHomework Practice sheet 2-1 evens only