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2-6. Prime Factorization. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 2-6. Prime Factorization. Course 2. 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.

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2-6

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  1. 2-6 Prime Factorization Course 2 Warm Up Problem of the Day Lesson Presentation

  2. 2-6 Prime Factorization Course 2 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

  3. Bellwork on slates • Write each expression using exponents • Example 7x7x7 = 73 • 1. 4x4x4x4x4x4 • 2. 3x3x3x3x3 • Write each expression as a product of repeated multiplication • Example 43 = 4x4x4 = 64 • 3. 53 • 4. 65 • 5. 114

  4. Bellwork • Write each expression using exponents • Example 7x7x7 = 73 • 1. 4x4x4x4x4x4 46 • 2. 3x3x3x3x3 35 • Write each expression as a product of repeated multiplication • Example 43 = 4x4x4 = 64 • 3. 53 125 • 4. 65 7776 • 5. 114 14641

  5. 2-6 Prime Factorization Course 2 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

  6. 2-6 Prime Factorization Course 2 Learn to find the prime factorizations of composite numbers.

  7. 2-6 Prime Factorization Course 2 Insert Lesson Title Here Vocabulary prime number – a number that has exactly two factors, 1 and itself. composite number – a number that has more than two factors prime factorization – a number written as a product of its prime factors.

  8. 2-6 Prime Factorization Course 2 In June 1999, Nayan Hajratwala discovered the first known prime number with more than one million digits. The new prime number, 26,972,593 – 1, has 2,098,960 digits. 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.

  9. 2-6 Prime Factorization Course 2 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.

  10. 2-6 Prime Factorization Course 2 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.

  11. 2-6 Prime Factorization Course 2 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.

  12. 2-6 Prime Factorization Course 2 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.

  13. 2-6 Prime Factorization Writing Math You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor. Course 2

  14. 2-6 Prime Factorization Course 2 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.

  15. 2-6 Prime Factorization Course 2 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.

  16. 2-6 Prime Factorization Course 2 Insert Lesson Title Here 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.

  17. 2-6 Prime Factorization Course 2 Insert Lesson Title Here 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.

  18. 2-6 Prime Factorization Course 2 You can also use a step diagram to find the prime factorization of a number. At each step, divide by the smallest possible prime number. Continue dividing until the quotient is 1.

  19. 2-6 Prime Factorization Course 2 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. 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.

  20. 2-6 Prime Factorization Course 2 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. 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.

  21. 2-6 Prime Factorization Course 2 Insert Lesson Title Here Check It Out: Example 3A Write the prime factorization of each number. 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.

  22. 2-6 Prime Factorization Course 2 Insert Lesson Title Here Check It Out: Example 3B Write the prime factorization of the number. 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.

  23. 2-6 Prime Factorization Course 2 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.

  24. 2-6 Prime Factorization Course 2 Insert Lesson Title Here Lesson Quiz: Part I Tell whether each number is prime or composite. 1. 23 2. 39 3. 27 prime composite composite

  25. 2-6 Prime Factorization Course 2 Insert Lesson Title Here 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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