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1.2 Prime Factorization Lesson Objective Vocabulary Le • Express a whole number as a product of its prime factors. composite number prime factor arn Identify composite numbers. Another way to represent a whole number is to write it as a product of its factors. Find all the factors of 18. 18 5 1 3 18 18 5 2 3 9 18 5 3 3 6 The factors of 18 are 1, 2, 3, 6, 9, and 18. The number 18 is an example of a composite number. A composite number has more than two different whole number factors. 18 has six factors, so it is a composite number. The number 3 is an example of a prime number. A prime number has only two factors, the number itself and 1. Le In the list of factors for 18, 2 and 3 are the only prime numbers. 2 and 3 are the prime factors of 18. arn Write a composite number as a product of its prime factors. A composite number can be written as a product using only its prime factors. This is known as prime factorization. For example, you can write 18 as a product using only its prime factors. 18 5 2 3 3 3 3 16 Chapter 1 Positive Numbers and the Number Line Math Note Finding the prime factorization of a number is not the same as finding the factors of a number. A composite number can be written as the product of different pairs of its factors. But there is one and only one prime factorization for a given composite number. Express 60 as a product of its prime factors. Method 1 Start dividing the number by 2 60 Divide by prime factor 2. its least prime factor. Continue 30 2 Divide by prime factor 2. dividing until the quotient is a 3 15 Divide by prime factor 3. prime number. 5 The prime factors of 60 are 2, 3, and 5. 60 5 2 3 2 3 3 3 5 Method 2 60 2 · 30 · 2 · 2 · 2 · 2 Math Note 15 3 · Another way to write multiplication is to use the multiplication dot. 5 So, 60 5 2 · 2 · 3 · 5 means 60 5 2 3 2 3 3 3 5. The prime factors of 60 are 2, 3, and 5. 60 5 2 · 2 · 3 · 5 Guided Practice Complete. 1 Express 48 as a product of its prime factors. Method 1 2 48 ? 48 24 2 2 · ? 2 · 2 · ? 2 · 2 · 2 · ? · 2 · 2 · 2 · ? ? Method 2 6 ? 48 5 2 3 ? 323 ? 3 ? 2 48 5 2 · 2 · 2 · 2 · ? ? Lesson 1.2 Prime Factorization 17 Practice 1.2 1 Copy the array of numbers. Circle all the prime numbers. 1 2 3 4 5 6 7 8 9 10 11 12 131415161718 192021222324 252627282930 Express each number as a product of its prime factors. 2 6 3 15 4 36 5 78 6 184 7 360 8 24 9 49 10 81 11 144 12 245 13 510 14 250 15 1,089 16 4,725 17 900 18 27,000 Solve. 19 Describe the steps for finding the prime factors of 42. 20 400 written as a product of its prime factors is 2 3 2 3 2 3 2 3 5 3 5. Write 800 as a product of its prime factors. 21 Given that 320 written as a product of its prime factors is 2 3 2 3 2 3 2 3 2 3 2 3 5, write 3,200 as a product of its prime factors. 22 2,700 written as a product of its prime factors is 2 3 2 3 3 3 3 3 3 3 5 3 5. Write 270 as a product of its prime factors. 23 It is given that 4,800 can be expressed in terms of its prime factors as 2 3 2 3 2 3 2 3 2 3 2 3 3 3 5 3 5. a) Write 1,200 as a product of its prime factors. b) Now, write 120 as a product of its prime factors. 18 Chapter 1 Positive Numbers and the Number Line