Prime Factorization ACTIVITY Factor Trees 1.3 SUGGESTED LEARNING STRATEGIES: Think/Pair/Share My Notes Th e prime factorization of a number shows the number as a product of factors that are all prime numbers. One way to fi nd the prime factorization of a number is to use a factor tree. • Use divisibility rules to fi nd two factors of the number. • Check whether the factors are prime or composite. • If both are prime, stop. If not, continue factoring until all factors are prime numbers. EXAMPLE 1 Find the prime factorization of 12. Step 1: Write 12. 12 Start with two factors of 12. Try 3 and 4. 3 × 4 Use branches to show the factors. Step 2: Check: 3 is a prime number, but 4 is not. 12 Continue by factoring 4. 3 × 4 Don’t forget to rewrite the 3 with the factors of 4. 3 × 2 × 2 Solution: Check again. All factors are now prime numbers, so this is the prime factorization of 12. TRY THESE Find the prime factorization of: a. 15 b. 16 © 2010 College Board. All rights reserved. 1. Will the prime factorization of 12 be diff erent if you start with the factors 2 and 6? Draw another factor MATH TERMS tree starting with 2 and 6. The Fundamental Theorem of Arithmetic states that any whole number greater than 1 can be written as a product of prime factors in only one way. The order of the factors may vary. Unit 1 • Number Concepts 15 0015-016_SB_MS1_1-3_SE.indd15-016_SB_MS1_1-3_SE.indd 1155 112/16/092/16/09 66:55:36:55:36 PPMM ACTIVITY 1.3 Prime Factorization continued FFactoractor TTreesrees SUGGESTED LEARNING STRATEGIES: Create Representations My Notes ACADEMIC VOCABULARY Prime factorization can be written two ways: • as the product of prime factors: 2 × 2 × 3 The prime factorization of a 2 number can be written using • using exponents: 2 × 3 exponents. An exponent tells how many times the base number is 2. Use factor trees to write the prime factorizations of 25 and 36. used as a factor. 34 Exponent Base 34 3 3 3 3 = × × × 3. Write each number using exponents. a. 2 × 2 × 2 × 3 × 3 b. 3 × 3 × 5 × 7 × 7 c. 2 × 3 × 3 × 13 × 13 × 13 4. Write the following numbers as products of prime factors. a. 24 b. 32 × 53 CHECK YOUR UNDERSTANDING Write your answers on notebook paper. 4. Write 48 as a product of prime factors and Show your work. then using exponents. 1. Write the prime factorization of 100. 5. Is 2 × 3 × 4 the prime factorization of 24? © 2010 College Board. All rights reserved. 2. Write the prime factorization of 72 using Explain your reasoning. exponents. 6. MATHEMATICAL How are 4 × 2 and 42 REFLECTION diff erent? Explain your 3. Write 3 2 × 43 as a product of prime factors. thinking. 16 SpringBoard® Mathematics with Meaning™ Level 1 0015-016_SB_MS1_1-3_SE.indd15-016_SB_MS1_1-3_SE.indd 1166 112/16/092/16/09 66:55:39:55:39 PPMM.