Name Date Class Reteach Factors and Greatest Common Factors A prime number has exactly two factors, itself and 1. The number 1 is riot a prime number. To write the prime factorization of a number, factor the number into its prime factors only. Find the prime factorization of 30. Choose any prime number that is a factor of 30. Then divide. 5[3Q 5[30 6 5 30 2 6 5J30 5 30 ^ _» 2[6_ 3 3 3 5[30 2\6_ 3[3_ 1 -». 30 = 5 2 3 Repeat the process with the quotient. The prime factorization of 30 is 2 3 5. Find the prime factorization of 84. 2 84 242 3 21 Check by multiplying: 7lZ 2 2 3 7-84 1 V. The prime factorization of 84 is 2 2 3 7 or 2 3 7. Fill in the blanks below to find the prime factorization of the given numbers. 2 44 1 2Q DQ1 2[56_ 2 Q. 2- DD an 3- DQ DQ1 an 3 81 4. 99 5. 75 6. 84 Copyright by Holt, Rinehart and Winston. Holt Algebra 1 All rights reserved.
Name Date Class Reteach Factors and Greatest Common Factors (continued) If two numbers have the same factors, the numbers have common factors. The largest of the common factors is called the greatest common factor, or GCF. Find the GCF of 12 and 18. Think of the numbers you multiply to equal 12. 1 X 12 = 12 ' 2X6 = 12 > The factors of 12 are: 1,2, 3, 4, 6, 12 3 x 4 = 12 i Think of the numbers you multiply to equal 18. 1X18 = 18 ' 2X9 = 18 > The factors of 18 are: 1, 2, 3, 6, 9, 18. 3 X6 = 18, The GCF of 12 and 18 is 6. Find the GCF of 8x2 and 10x. The factors of 8x2 are: 1, 2, 4, 8, x, x The factors of 10x are: 1, 2, 5, 10, x I The GCF of 8x2 and 10x is 2x. Find the GCF of 28 and 44 by following the steps below. 7. Find the factors of 28. _ 8. Find the factors of 44. _ 9. Find the GCF of 28 and 44. _ Find the GCF of each pair of numbers. 10. 15 and 20 11. 16 and 28 12. 24 and 60 Find the GCF of each pair of monomials. 13. 4aand 10a 14. 15x3and21x2 15. 5y2 and 8y iht by Holt, Rinehart and Winston. All Vfghts reserved. Holt Algebra 1
Name Date Class. isspfi Practice B K Ui Factors and Greatest Common Factors ~ 1. 18 2. 120 3. 56 4. 390 5. 144 6. 153 Find the GCF of each pair of numbers.. J 6 and 20 8. 9 and 36 9. 15 and 28 10. 35 and 42 11. 33 and 66 12. 100 and 120 ^3. 78 and 30 14. 84 and 42 Find the GCF of each pair of monomials. 15. 15x4and35x2 16. 12p2 and 30g5 17. -6f3and9f 18. 27y3zand45x2y 19. 12atoand12 20. -3d3 and Ud4 21. -mv and 3m6n 22. ^Qgh^ and 5/7 2. Kirstin is decorating her bedroom wall with photographs. She has 36 photographs of family and 28 photographs of friends. She wants to arrange the photographs in rows so that each row has the same number of photographs, and photographs of family and photographs of friends do not appear in the same row. a. How many rows will there be if Kirstin puts the greatest possible number of photographs in each row? b. How many photographs will be in each row? Copyright by Holt, Rinehart and Winston. A Hdlt All rights reserved. ^ ii«n
Name Date Class. LESSON Practice C Factors and Greatest Common Factors 1. 75 2. 160 3. 3500 Find the GCF of each set of numbers. 4. 18 and 36 5. 54 and 60 6. 30 and 49 7. 72 and 54 8. 12, 18, and 30 9. 8, 20, and 28 10. 15, 20, and 42 11. 16, 24 and 56 Find the GCF of each set of monomials. 12. 21m3 and 28m 13. 13xand26 14. 8x2y and -12x3y2 15. 30sY and 36s3f5_ 16. 18f5, 120s4, and 30f2 17. 4x2, 2x6, and -x3_ 18. -6m5, 5n6, and 8n 19. 35y4z, -14y3z2, and -7y2 20. Emilio has 30 oranges, 45 apples, and 20 pears with which to make fruit baskets. He wants each fruit basket to contain the same number of each type of fruit. If he puts the greatest possible number of each type of fruit into each basket, how many fruit baskets can he make? How many pieces of each type of fruit will be in each basket? 21. Nina is babysitting a little boy who has a collection of small vehicles. He has 36 cars, 12 vans, and 27 trucks. The boy is trying to line up the vehicles in rows, with the same number of vehicles in each row. He does not want different types of vehicles to be in the same row. Describe the arrangement of the rows if Nina helps the boy put the greatest possible number of vehicles in each row. Copyright by Holt, Rinehart and Winston. 5 Holt AlQ8bf3 1 All nghts reserved.
3 7.) I, II.) Problem Solving 1. x2-16; $128 2. OJSx2 - x- 65; 2575 square feet 3.x2-144 in2 4. D 5. G 6. A 7. G Reading Strategies 1. difference of squares 2. perfect square trinomial 3. It will have 3 terms. 4. c4 + 20c2d+100d2; perfect square trinomial 5. 4s2-9; difference of squares LESSON 8-1, i (/ 1r 5. 24 32 7. 4 9. 1 11. 33 13. 6 15. 5X2 17. 3f 19. 12 21. m6n 23. a. 16 b. 4 Practice C 1. 3 52 3. 22 53 7 5 C 7. 18 9. 4 11. 8 13. 13 15. 6s 17.x2 19. 6. 32-17 8. 9 10. 7 12. 20 14. 42 16. 6 18. 9y 20. 2C/3 22. 5h 2. 25 5 4. 18 6 4. I 8. 6 10. 1 12. 7m 14. 4xV 16. 6 18. 1 20. 5 baskets; each will have 6 oranges, 9 apples, and 4 pears. 21. There will be 25 rows with 3 vehicles in each row. There will be 12 rows of cars, 4 rows of vans, and 9 rows of trucks. Review for Mastery 1-2 44 IS) Practice B 1. 2'32 3. 23>7 2. 23 3 5 4. 2.3.5.13 Original content Copyright by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A12 Holt McDougal Algebra 1