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Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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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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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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**Sunshine State Standards**

Prep for MA.7.A.3.2 Add, subtract, multiply, and divide…fractions… Review MA.5.A.2.4

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Vocabulary prime number composite number prime factorization

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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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**A composite number is a whole number that has more than two factors**

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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**Additional Example 1: Identifying Prime and Composite Numbers**

Tell whether each number is prime or composite. A. 11 B. 16 The factors of 11 are 1 and 11. The factors of 16 are 1, 2, 4, 8, and 16. 11 is prime. 16 is composite.

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

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**A composite number can be written as the product of its prime factors**

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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**You can write prime factorization by using exponents**

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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**Additional Example 2A: Using a Factor Tree to Find Prime Factorization**

Write the prime factorization of each number. 24 Write 24 as the product of two factors. 24 8 · 3 Continue factoring until all factors are prime. 4 · 2 · 3 2 · 2 · 2 · 3 The prime factorization of 24 is 2 · 2 · 2 · 3 or 23 · 3.

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**Additional Example 2B: Using a Factor Tree to Find Prime Factorization**

Write the prime factorization of each number. 150 150 Write 150 as the product of two factors. 30 · 5 Continue factoring until all factors are prime. 10 · 3 · 5 2 · 5 · 3 · 5 The prime factorization of 150 is 2 · 3 · 5 · 5, or 2 · 3 · 52.

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Check It Out: Example 2A Write the prime factorization of each number. 36 Write 36 as the product of two factors. 36 18 · 2 Continue factoring until all factors are prime. 9 · 2 · 2 3 · 3 · 2 · 2 The prime factorization of 36 is 2 · 2 · 3 · 3 or 22 · 32.

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Check It Out: Example 2B Write the prime factorization of the number. 90 90 Write 90 as the product of two factors. 45 · 2 Continue factoring until all factors are prime. 9 · 5 · 2 3 · 3 · 5 · 2 The prime factorization of 90 is 3 · 3 · 5 · 2, or 2 · 32 · 5.

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**You can also use a step diagram to find a 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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**Additional Example 3A: Using a Step Diagram to Find Prime Factorization**

Write the prime factorization of each number. 476 Divide 476 by 2. Write the quotient below 476. 2 476 2 238 Keep dividing by a prime number. 7 119 17 17 1 Stop when the quotient is 1. The prime factorization of 476 is 2 · 2 · 7 · 17, or 22 · 7 · 17.

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**Additional Example 3B: Using a Step Diagram to Find Prime Factorization**

Write the prime factorization of the number. 275 Divide 275 by 5. Write the quotient below 275. 5 275 5 55 11 11 Stop when the quotient is 1. 1 The prime factorization of 275 is 5 · 5 · 11, or 52 · 11.

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Check It Out: Example 3A Write the prime factorization of each number. 324 Divide 324 by 2. Write the quotient below 324. 2 324 2 162 Keep dividing by a prime number. 3 81 3 27 3 9 Stop when the quotient is 1. 3 3 1 The prime factorization of 324 is 2 · 2 · 3 · 3 · 3 · 3, or 22 · 34.

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Check It Out: Example 3B Write the prime factorization of the number. 325 Divide 325 by 5. Write the quotient below 325. 5 325 5 65 13 13 Stop when the quotient is 1. 1 The prime factorization of 325 is 5 · 5 · 13, or 52 · 13.

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**There is only one prime factorization for any given composite number**

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. 2 476 7 476 2 238 2 68 7 119 2 34 17 17 17 17 1 1 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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Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

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Lesson Quiz: Part II Write the prime factorization of each number. 4. 27 5. 36 6. 28 7. 132 8. 52 9. 108 33 22 · 32 22 · 7 22 · 3 · 11 22 · 13 22 · 33

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**Lesson Quiz for Student Response Systems**

1. Which of the following is a prime number? A. 107 B. 108 C. 111 D. 112

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**Lesson Quiz for Student Response Systems**

2. Which of the following is a composite number? A. 103 B. 107 C. 108 D. 109

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**Lesson Quiz for Student Response Systems**

3. Which of the following is a composite number? A. 131 B. 133 C. 137 D. 109

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**Lesson Quiz for Student Response Systems**

4. Identify the prime factorization of 125. A. 52 B. 33 C. 53 D. 73

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**Lesson Quiz for Student Response Systems**

5. Identify the prime factorization of 45. A. 5 · 9 B. 32 · 5 C. 23 · 5 D. 3 · 15

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