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2. Warm Up – write in your notes for today

Welcome to math! Thursday, July 28 th , 2011. 1. Turn in your syllabus and e-mail verification form on the front table if you have not already done so. 2. Warm Up – write in your notes for today

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2. Warm Up – write in your notes for today

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  1. Welcome to math! Thursday, July 28th, 2011 1.Turn in your syllabus and e-mail verification form on the front table if you have not already done so. 2. Warm Up – write in your notes for today Write each number as a product of two whole numbers in as many ways as possible (write the fact families). 1.6 2. 16 3. 17 4. 36 5. 23 1 x 6, 2 x 3 1 x 16, 2 x 8, 4 x 4 1 x 17 1 x 36, 2 x 18, 3 x 12, 4 x 9, 6 x 6 1 x 23 3. Objective: Find the prime factorizations of composite numbers. (write in notes) 4. Definitions: prime number, composite number and prime factorization. 5. Grab a whiteboard if you have your own marker and eraser. 6. Work on your MyFace Activity when finished.

  2. Insert Lesson Title Here Vocabulary prime number composite number prime factorization

  3. A prime numberis 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.

  4. 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. 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.

  5. Additional Example 2A & 2B: Identifying Prime and Composite Numbers Tell whether each number is prime or composite. A. 23 divisible by 1, 23 prime B. 48 divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. composite

  6. Additional Example 2C & 2D: Identifying Prime and Composite Numbers Tell whether each number is prime or composite. C. 31 divisible by 1, 31 prime D. 18 divisible by 1, 2, 3, 6, 9, 18 composite

  7. Try This: Example 2A & 2B Tell whether each number is prime or composite. A. 27 divisible by 1, 3, 9, 27 composite B. 24 divisible by 1, 2, 3, 4, 6, 8, 12, 24 composite

  8. Example 1: Using a Factor Tree to Find Prime Factorization Write the prime factorization of the number. A. 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. Using exponents, you can write this as 23 · 3.

  9. Example B: Using a Factor Tree to Find Prime Factorization Write the prime factorization of the number. B. 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.

  10. Insert Lesson Title Here Try This: Example 1A Write the prime factorization of the number. A. 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. Using exponents, you can write this as 22 · 32.

  11. Insert Lesson Title Here Try This: Example 1B Write the prime factorization of the number. B. 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.

  12. You can also use a step diagramto find the prime factorization of a number… • Steps for Using the Step Diagram for Prime Factorization • At each step, divide by the smallest possible prime number. • Continue dividing until the quotient is 1. • The prime factors of the number are the prime numbers you divided by.

  13. Example 3: Using a Step Diagram to Find Prime Factorization Write the prime factorization of each number. A. 476 Divide 476 by 2. Write the quotient below 476. 476 2 238 2 Keep dividing by a prime number. 119 7 17 17 1 Stop when the quotient is 1. The prime factorization of 476 is 2 · 2 · 7 · 17, or 22 · 7 · 17.

  14. Additional Example 2B: Using a Step Diagram to Find Prime Factorization Write the prime factorization of the number. B. 275 Divide 275 by 5. Write the quotient below 275. 275 5 55 5 11 11 Stop when the quotient is 1. 1 The prime factorization of 275 is 5 · 5 · 11, or 52 · 11.

  15. Insert Lesson Title Here Try This: Example 4 Write the prime factorization of each number. A. 324 Divide 324 by 2. Write the quotient below 324. 324 2 162 2 Keep dividing by a prime number. 81 3 27 3 9 3 Stop when the quotient is 1. 3 3 1 The prime factorization of 324 is 2 · 2 · 3 · 3 · 3 · 3, or 22 · 34.

  16. Insert Lesson Title Here Try This: Example 2B Write the prime factorization of the number. B. 325 Divide 325 by 5. Write the quotient below 325. 325 5 65 5 13 13 Stop when the quotient is 1. 1 The prime factorization of 325 is 5 · 5 · 13, or 52 · 13.

  17. 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. 476 476 2 7 238 68 2 2 119 34 7 2 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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