Prime Factorization • • • Prime Factorization of Anumber Afactor Isto Use Tree

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B © 2010 College Board. All rights reserved. _ M S 1 _ 1 - 3 _ 1. a. Find prime the factorization of: TRY THESE Solution: Step 2: Step 1: Find prime the factorization of 12. EXAMPLE 1 Th SUGGESTED LEARNING STRATEGIES: Think/Pair/Share Factor Trees Prime Factorization • • • prime factorization of anumber afactor isto use tree. product of factors that are allprime numbers. Oneway to fi S E e . 15 i n d tree starting with 2and 6. factorsthe 2and 6?Draw another factor Will prime the factorization of diff 12be are prime numbers. If are both prime, stop. If not, continue factoring until allfactors factors the Check whether are prime or composite. Use divisibility to fi rules d prime factorization

1 Check: 3isaprime number, but Write 12. 5 Check again. Allfactors are now prime numbers, is this so 4 isnot. the primethe factorization of 12. with thefactors of 4. Don’t forget to rewrite the3 Continue by factoring 4. Use branches to show factors. the Try 3and 4. Start with two factors of 12. of anumber shows number the asa nd two factors of number. the b. 16 erent ifyou with start 3 × 3 3 12 2 12 × × 4 4 × nd the 2 order ofthefactorsmayvary. factors inonlyoneway.The written asaproductofprime number greaterthan1canbe Arithmetic The MATH TERMS Unit 1• Fundamental Theoremof My Notes statesthatanywhole Number Concepts ACTIVITY 1.3 112/16/09 6:55:36 PM 15 2 / 1 6 / 0 9

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P M 0015-016_SB_MS1_1-3_SE.indd 16 1 5 - 0 1 6 _ S 16 B continued ACTIVITY _ 3 used asafactor. many timesthebasenumberis exponents. An number canbewrittenusing The primefactorizationofa ACADEMIC VOCABULARY M CHECK YOURUNDERSTANDING 3. 2. 1. Show your work. Write your answerson paper. notebook S 1 _ SpringBoard 1 Base - Write 3 Write exponents. Write prime the factorization of 72using Write prime the factorization of 100. 3 3 _ S E 4 . i n = d d 1.3 3

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T r e e s a. 4. c. b. a. 3. 2. b. • using product asthe of prime factors: 2 • Prime factorization can written be two ways: Write eachnumber using exponents. Use factor trees to write theprime factorizations of 25and 36. Write following the numbers asproducts of prime factors. Level1 3 2 2 2 Representations SUGGESTED LEARNING STRATEGIES: Create 3 2 4 exponents × × ×

× 3 2 3 5 × × × 3 5 2 3 × × × : 2 7 3 13 6. 5. 4. 2 × ×

× × Explain your reasoning. Is 2 usingthen exponents. Write 48 asaproduct of prime factors and thinking. 7 3 REFLECTION MATHEMATICAL 3 13 × × 3 13 × 4 the prime 4the factorization of 24? × 2

× How are 4 diff 3 erent? Explain your × 2and 4 2

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