1. Copyright © Ed2Net Learning, Inc.1 Prime Factorization Grade 6

2. Copyright © Ed2Net Learning, Inc. 2 WARM UP 1.10 3 = 2. p3rrrp3 = 3. 4 0 = 4. 8 5 =

3. Copyright © Ed2Net Learning, Inc. 3 Lets review what we have learned in the last Lesson The exponent is sometimes referred to as the power 8989 Base Exponent

4. Copyright © Ed2Net Learning, Inc. 4 7 3 means to multiply the base 7 by itself 3 times 7373 7 3 = 7 x 7 x 7 Review

5. Copyright © Ed2Net Learning, Inc. 5 In the Real World Dancers A dance teacher is planning a dance for a show. The dancers will be arranged in rows with the same number of dancers in each row. Can a group of 12 dancers or a group of 14 dancers be arranged in more ways? Prime Factorization

6. Copyright © Ed2Net Learning, Inc. 6 Finding Factors EXAMPLE 1 To answer the previous question, list all the factors of 12 and 14 by writing each number as a product of two numbers in as many ways as possible. The factors of 12 are: 12: 1  12 2  6 3  4 4  3 1,3,4,6, and 12. 2, Prime Factorization Stop when a pair of factors repeat.

7. Copyright © Ed2Net Learning, Inc. 7 Finding Factors EXAMPLE 1 To answer the previous question, list all the factors of 12 and 14 by writing each number as a product of two numbers in as many ways as possible. 14: 1  14 2  7 7  2 The factors of 12 are: The factors of 14 are: 12: 1  12 2  6 3  4 4  3 1,3,4,6, and 12. 2, 1,2,7, and 14. Prime Factorization Stop when a pair of factors repeat. A group of 12 dancers can be arranged in more ways than a group of 14 dancers, because 12 has more factors than 14. ANSWER

8. Copyright © Ed2Net Learning, Inc. 8 Divisibility A number is divisible by another number if that other number is a factor of the first. Divisibility rules can help you find factors. Prime Factorization

9. Copyright © Ed2Net Learning, Inc. 9 NOTE BOOK Divisibility Rules for 2, 3, 5, 6, 9, and 10 A whole number is divisible by:  2 if the number is even.  5 if it ends with 5 or 0.  6 if it is even and is divisible by 3.  10 if it ends with 0. Divisibility A number is divisible by another number if that other number is a factor of the first. Divisibility rules can help you find factors. Prime Factorization  9 if the sum of its digits is divisible by 9.  3 if the sum of its digits is divisible by 3.

10. Copyright © Ed2Net Learning, Inc. 10 Using Divisibility Rules EXAMPLE 2 Test 150 for divisibility by 2, 3, 5, 6, 9, and 10. 150 is even, 1 + 5 + 0 = 6, 150 ends with 0, 150 is even and divisible by 3, 150 is divisible by 2, 3, 5, 6 and 10, but not by 9. so it is divisible by 2. So, 150 is divisible by 3, but not divisible by 9. so it is divisible by 5 and by 10. so it is divisible by 6. ANSWER Prime Factorization and 6 is divisible by 3, but not 9.

11. Copyright © Ed2Net Learning, Inc. 11 Your Turn! List all the factors of the number. 8 9 15 18

12. Copyright © Ed2Net Learning, Inc. 12 Your Turn! Test the number for divisibility by 2, 3, 5, 6, 9, and 10. 100 456 783 1584

13. Copyright © Ed2Net Learning, Inc. 13 Prime Factorization Primes and Composites A prime number is a whole number greater than 1 whose only factors are 1 and itself. A composite number is a whole number greater than 1 that has factors other than 1 and itself. The number 1 is neither prime nor composite.

14. Copyright © Ed2Net Learning, Inc. 14 Classifying as Prime or Composite Tell whether the number is prime or composite. 51 SOLUTION List the factors of 51: The number 51 is composite. It has factors other than 1 and itself. EXAMPLE 3 1,3,17,51. ANSWER Prime Factorization

15. Copyright © Ed2Net Learning, Inc. 15 Classifying as Prime or Composite Tell whether the number is prime or composite. 51 59 SOLUTION List the factors of 51: List the factors of 59: The number 59 is prime. Its only factors are 1 and itself. 1, The number 51 is composite. It has factors other than 1 and itself. EXAMPLE 3 1,3,17,51.59. ANSWER Prime Factorization SOLUTION

16. Copyright © Ed2Net Learning, Inc. 16 Your Turn! Tell whether the number is prime or composite. 11 13 14 35

17. Copyright © Ed2Net Learning, Inc. 17 Prime Factorization Prime Factorization Writing the prime factorization of a number means writing the number as the product of prime numbers. You can use a diagram called a factor tree to write a factorization of a number. To write the prime factorization, continue factoring until only prime factors appear in the product.

18. Copyright © Ed2Net Learning, Inc. 18 Writing a Prime Factorization Write the prime factorization of 180. 180 1810  22335  2925  The prime factorization of 180 is 2 2  3 2  5. EXAMPLE 4 Write the original number. Factor 180 as 10 times 18. Factor 10 and 18. Factor 9. ANSWER Prime Factorization

19. Copyright © Ed2Net Learning, Inc. 19 Writing a Prime Factorization Write the prime factorization of 180. 180 1810  22335  2925  The prime factorization of 180 is 2 2  3 2  5. Use multiplication to check your answer. C HECK 2 2  3 2  5 = 4  9  5 = 180 EXAMPLE 4 Write the original number. Factor 180 as 10 times 18. Factor 10 and 18. Factor 9. ANSWER Prime Factorization

20. Copyright © Ed2Net Learning, Inc. 20 Your Turn! Complete the factor tree. Then write the prime factorization. 42 ? X ? 2 X ? X 7 68 2 X ? ? X 2 X ? 81 ? X 9 ? X 3 X ? X 3

21. Copyright © Ed2Net Learning, Inc. 21 Let us take a break!!!

22. Copyright © Ed2Net Learning, Inc. 22

23. Copyright © Ed2Net Learning, Inc. 23 Sandcastle Day has been an annual event in Cannon Beach, Oregon, since 1964. Entrants from each age division are given plots measuring 81 square feet, 225 square feet or 441 square feet, on which to build their sand castles. Find the prime factorization of 81, 225, 441. Word Problems

24. Copyright © Ed2Net Learning, Inc. 24 Ben is ordering cartons to ship Jenga games to retail stores. The height, width and length of the cartons could be 2 packages high, 3 packages wide and 4 packages long. Such a carton would contain 24 packages of games. List two other ways to arrange 24 packages. Word Problems

25. Copyright © Ed2Net Learning, Inc. 25 Find the mystery number from the following clues This whole number is between 30 and 40 It has only two prime factors The sum of its prime factors is 5 Word Problems

26. Copyright © Ed2Net Learning, Inc. 26 Assessment List the factors of the number. 1. 14 2. 19 Test the number for divisibility by 2, 3, 5, 6, 9, and 10. 3. 140 4. 282 Tell whether a number is prime or composite. 5. 7 6. 37

27. Copyright © Ed2Net Learning, Inc. 27 Assessment Write the prime factorization of the number. 7. 39 8. 63 Find the least number that is divisible by the given numbers. 9. 2, 3, and 5 10. 6, 9, and 10

28. Copyright © Ed2Net Learning, Inc. 28 Prime numbers- whole number greater than 1 that is only divisible by itself and 1. that is only divisible by itself and 1. Composite Numbers – whole number greater than 1 that has more than 2 factors Prime Factorization – expressing a composite number as a product of prime numbers Lets Review what we have learned today

29. Copyright © Ed2Net Learning, Inc. 29 Methods for finding Prime Factorization 460 460 10 * 46 10 * 46 2 * 5 23 * 2 2 * 5 23 * 2 460 =2 * 2 * 5 * 23 Prime factors are 2² * 5 * 23 Prime factors are 2² * 5 * 23 Factor Tree Method

30. Copyright © Ed2Net Learning, Inc. 30 Note that 2, 3 and 5 are factors of 60 and all these factors are prime numbers. We call them prime factors. When we express a number as a product of prime factors, we have actually factored it completely. We refer to this process as prime factorization The number 60 is a composite number. It can be written as the product 2 x 2 x 3 x 5.

31. Copyright © Ed2Net Learning, Inc. 31 Great Job Today! Remember to practice what you have learned!