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EXERCISES
For more exercises, see Extra Practice.
Practice and Problem Solving
A
Practice by Example
Example 1
(page 186)
Example 2
(page 187)
Example 3
(page 187)
B
Apply Your Skills
State whether each number is prime or composite. Explain.
1. 27
2. 19
3. 31
4. 38
5. 45
6. 53
7. 87
8. 93
Write the prime factorization of each number.
9. 8
10. 49
11. 34
12. 42
13. 360
14. 115
15. 186
16. 621
Use prime factorization to find each GCF.
17. 10, 45
18. 14, 21
19. 25, 100
20. 57, 84
21. 14c 2, 35c
22. 3y 2, 24y 3
23. 18c 3, 24c 3
24. 6m 3n, 8mn 2
Is each number prime, composite, or neither? For each composite
number, write the prime factorization.
25. 17
26. 1
27. 49
28. 522
29. Organization A math teacher and a science teacher combine
their first-period classes for a group activity. The math class has
24 students and the science class has 16 students. The teachers need
to divide the students into groups of the same size. Each group must
have the same number of math students. Find the greatest number
of groups possible.
Find each GCF.
30. 6, 8, 12 2
31. 42, 65
32. 54, 144
33. 8, 16, 20
34. 12, 18, 21
35. 143, 169
36. z, z2
37. 180a2, 210a
38. x2y, xy2
39. a3b, a2b2
40. c3df 2, c2d2f 41. a2b, b2c, ac 2
a
42. Reasoning Find the integers that fit the following conditions:
• They are between 44 and 53.
• The sums of their digits are prime.
• They have more than three factors.
? 29
43. Open-Ended The GCF of 36 and x is 6. What are two possible
values for x?
44. Seating Arrangements Organizers for a high school graduation
have set up chairs in two sections. They put 126 chairs for
graduates in the front section and 588 chairs for guests in the
back section. If all rows have the same number of chairs, what is
the greatest number of chairs possible for a row?
4-3 Prime Factorization and Greatest Common Factor
189-190
C
Challenge
Is each number prime, composite, or neither? For each composite
number, write the prime factorization.
45. 253
46. 1,575
47. 1,003
48. 283
Two numbers are relatively prime if their GCF is 1. Are the numbers
in each pair below relatively prime? Explain.
SAMPLE
8, 17 Yes, 8 and 17 are relatively prime. The GCF is 1.
7, 35 No, 7 and 35 are not relatively prime. The GCF is 7.
49. 3, 20
50. 9, 42
51. 13, 52
52. 24, 47
53. 52, 65
54. 63, 74
55. 15, 22
56. 42, 72
57.
Explain how to find the prime factorization of 50.
Test Prep
Multiple Choice
Take It to the NET
Online lesson quiz at
www.PHSchool.com
Web Code: ada-0403
Extended Response
In Exercises 58 and 59, what is the GCF of each given pair?
58. 27x 2 y 3 and 46x 2y C
A. 3x2y
B. x2y2
C. x2y
D. 9x2y
59. 25b 2c and 42bc G
F. bc2
G. bc
H. b2c
I. b2c2
60. For which pair is the GCF 12? B
A. 3, 4
B. 24x2, 36y
C. 12xy, 24y
D. 3x, 12x
61. Simon is covering a wall with equal-sized tiles that cannot be cut
into smaller pieces. The wall is 66 inches high by 72 inches wide.
What is the area of the largest square tile that Simon can use? H
F. 9 in.2
G. 16 in.2
H. 36 in.2
I. 64 in.2
62. a. Is the product of two prime numbers also prime?
b. Justify your answer. c. Give an example.
Mixed Review
Lesson 4-2
Evaluate for x 5 2 and y 5 5.
63. x 2 y
Lesson 3-6
Lesson 2-7
189-190
64. xy 2
65. x 2 + y 2
66. x 4 - y
Solve each equation.
67. 3x = 5.4
68. -0.5a = 4.35
69. 4.32 = 1.6y
70. -8m = -74.4
71. Bookstore A store manager ordered three times as many books
as magazines. She ordered a total of 108 books and magazines.
How many books did she order?
Chapter 4 Factors, Fractions, and Exponents