Section 2.2 Prime Numbers and Factorization 113 52. Use the sieve of Eratosthenes to find the prime numbers less than 80. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 Concept 4: Prime Factorization For Exercises 53–56, determine whether or not the factorization represents the prime factorization. If not, explain why. 53. 54. 55. 56. 36 2 2 9 48 2 3 8 210 5 2 7 3 126 3 7 3 2 For Exercises 57–68, find the prime factorization. (See Examples 4 and 5.) 57. 70 58. 495 59. 260 60. 175 61. 147 62. 102 63. 138 64. 231 65. 616 66. 364 67. 47 68. 41 Concept 5: Identifying All Factors of a Whole Number For Exercises 69–76, list all the factors of the number. (See Example 6.) 69. 12 70. 18 71. 32 72. 55 73. 81 74. 60 75. 48 76. 72 Expanding Your Skills For Exercises 77–80, determine whether the number is divisible by 4. Use the following divisibility rule: A whole number is divisible by 4 if the number formed by its last two digits is divisible by 4. 77. 230 78. 1046 79. 4616 80. 10,264 For Exercises 81–84, determine whether the number is divisible by 8. Use the following divisibility rule: A whole number is divisible by 8 if the number formed by its last three digits is divisible by 8. 81. 1032 82. 2520 83. 17,126 84. 25,058 For Exercises 85–88, determine whether the number is divisible by 9. Use the following divisibility rule: A whole number is divisible by 9 if the sum of its digits is divisible by 9. 85. 396 86. 414 87. 8453 88. 1587 For Exercises 89–92, determine whether the number is divisible by 6. Use the following divisibility rule: A whole number is divisible by 6 if it is divisible by both 2 and 3 (use the divisibility rules for 2 and 3 together). 89. 522 90. 546 91. 5917 92. 6394
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