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2-7 Prime Factorization Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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2-7 Prime Factorization Warm Up Write each number as a product of two whole numbers in as many ways as possible. 1. 6 2. 16 3. 17 4. 36 1 · 6, 2 · 3 1 · 16, 2 · 8, 4 · 4 1 · 17 1 · 36, 2 · 18, 3 · 12, 4 · 9, 6 · 6

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2-7 Prime Factorization Problem of the Day Nicholas bikes every third day and skates every other day. On April 5 Nicholas biked and skated. When will he do both again? April 11

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2-7 Prime Factorization Prep for MA.7.A.3.2 Add, subtract, multiply, and divide…fractions… Review MA.5.A.2.4 Sunshine State Standards

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2-7 Prime Factorization Vocabulary prime number composite number prime factorization

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2-7 Prime Factorization A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself. Three is a prime number because its only factors are 1 and 3.

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2-7 Prime Factorization A composite number is a whole number that has more than two factors. Six is a composite number because it has more than two factors—1, 2, 3, and 6. The number 1 has exactly one factor and is neither prime nor composite.

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2-7 Prime Factorization Tell whether each number is prime or composite. Additional Example 1: Identifying Prime and Composite Numbers A. 11 11 is prime. The factors of 11 are 1 and 11. B. 16 16 is composite. The factors of 16 are 1, 2, 4, 8, and 16.

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2-7 Prime Factorization Tell whether each number is prime or composite. Check It Out: Example 1 A. 14 14 is composite. The factors of 14 are 1, 2, 7, and 14. B. 7 7 is prime. The factors of 7 are 1 and 7.

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2-7 Prime Factorization A composite number can be written as the product of its prime factors. This is called the prime factorization of the number. You can use a factor tree to find the prime factors of a composite number.

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2-7 Prime Factorization You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor. Writing Math

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2-7 Prime Factorization Write the prime factorization of each number. Additional Example 2A: Using a Factor Tree to Find Prime Factorization 24 8 · 3 4 · 2 · 3 2 · 2 · 2 · 3 Write 24 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 24 is 2 · 2 · 2 · 3 or 2 3 · 3.

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2-7 Prime Factorization Write the prime factorization of each number. Additional Example 2B: Using a Factor Tree to Find Prime Factorization 150 30 · 5 10 · 3 · 5 2 · 5 · 3 · 5 Write 150 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 150 is 2 · 3 · 5 · 5, or 2 · 3 · 5 2.

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2-7 Prime Factorization Check It Out: Example 2A Write the prime factorization of each number. 36 18 · 2 9 · 2 · 2 3 · 3 · 2 · 2 Write 36 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 36 is 2 · 2 · 3 · 3 or 2 2 · 3 2.

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2-7 Prime Factorization Check It Out: Example 2B Write the prime factorization of the number. 90 45 · 2 9 · 5 · 2 3 · 3 · 5 · 2 Write 90 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 90 is 3 · 3 · 5 · 2, or 2 · 3 2 · 5.

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2-7 Prime Factorization You can also use a step diagram to find a prime factorization. At each step, divide by a prime factor until the quotient is 1.

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2-7 Prime Factorization Write the prime factorization of each number. Additional Example 3A: Using a Step Diagram to Find Prime Factorization 476 238 119 17 1 2 2 7 Divide 476 by 2. Write the quotient below 476. Keep dividing by a prime number. Stop when the quotient is 1. The prime factorization of 476 is 2 · 2 · 7 · 17, or 2 2 · 7 · 17.

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2-7 Prime Factorization Write the prime factorization of the number. Additional Example 3B: Using a Step Diagram to Find Prime Factorization 275 55 11 1 5 5 Divide 275 by 5. Write the quotient below 275. Stop when the quotient is 1. The prime factorization of 275 is 5 · 5 · 11, or 5 2 · 11.

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2-7 Prime Factorization Check It Out: Example 3A Write the prime factorization of each number. 324 162 81 27 1 2 2 3 3 Divide 324 by 2. Write the quotient below 324. Keep dividing by a prime number. Stop when the quotient is 1. The prime factorization of 324 is 2 · 2 · 3 · 3 · 3 · 3, or 2 2 · 3 4. 9 3 3 3

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2-7 Prime Factorization Check It Out: Example 3B Write the prime factorization of the number. 325 65 13 1 5 5 Divide 325 by 5. Write the quotient below 325. Stop when the quotient is 1. The prime factorization of 325 is 5 · 5 · 13, or 5 2 · 13.

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2-7 Prime Factorization There is only one prime factorization for any given composite number. Example 2A began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result. 476 238 119 17 1 2 2 7 476 68 34 17 1 7 2 2 The prime factorizations are 2 · 2 · 7 · 17 and 7 · 2 · 2 · 17, which are the same as 17 · 2 · 2 · 7.

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2-7 Prime Factorization Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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2-7 Prime Factorization Lesson Quiz: Part I Tell whether each number is prime or composite. 1. 23 2. 39 3. 27 composite prime composite

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2-7 Prime Factorization Lesson Quiz: Part II Write the prime factorization of each number. 4. 27 5. 36 6. 28 7. 132 8. 52 9. 108 2 2 · 3 2 3 2 2 · 7 2 2 · 3 · 11 2 2 · 13 2 2 · 3 3

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2-7 Prime Factorization 1. Which of the following is a prime number? A. 107 B. 108 C. 111 D. 112 Lesson Quiz for Student Response Systems

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2-7 Prime Factorization 2. Which of the following is a composite number? A. 103 B. 107 C. 108 D. 109 Lesson Quiz for Student Response Systems

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2-7 Prime Factorization 3. Which of the following is a composite number? A. 131 B. 133 C. 137 D. 109 Lesson Quiz for Student Response Systems

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2-7 Prime Factorization 4. Identify the prime factorization of 125. A. 5 2 B. 3 3 C. 5 3 D. 7 3 Lesson Quiz for Student Response Systems

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2-7 Prime Factorization 5. Identify the prime factorization of 45. A. 5 · 9 B. 3 2 · 5 C. 2 3 · 5 D. 3 · 15 Lesson Quiz for Student Response Systems

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