Prime Factorization Worksheet

Name: ____________________________
Class: ____________________________
Date: ____________________________

Quick Review

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Prime factorization means writing a whole number as a product of prime numbers.

Example: 24 = 2 × 2 × 2 × 3 = 2³ × 3

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A. Find the Prime Factorization

Write each number as a product of prime factors.

1. 12 = __________________________
2. 18 = __________________________
3. 20 = __________________________
4. 24 = __________________________
5. 30 = __________________________
6. 36 = __________________________
7. 40 = __________________________
8. 42 = __________________________
9. 45 = __________________________
10. 48 = __________________________
11. 50 = __________________________
12. 54 = __________________________
13. 56 = __________________________
14. 60 = __________________________
15. 63 = __________________________
16. 72 = __________________________
17. 75 = __________________________
18. 80 = __________________________
19. 84 = __________________________
20. 90 = __________________________

B. Use Exponents

Write the prime factorization using exponents.

21. 16 = __________________________
22. 32 = __________________________
23. 64 = __________________________
24. 72 = __________________________
25. 100 = _________________________
26. 108 = _________________________
27. 120 = _________________________
28. 125 = _________________________
29. 144 = _________________________
30. 150 = _________________________

C. Find the Missing Prime Factor

31. 24 = 2 × 2 × ______ × 3
32. 36 = 2 × 2 × 3 × ______
33. 40 = 2 × 2 × ______ × 5
34. 45 = 3 × 3 × ______
35. 54 = 2 × 3 × 3 × ______
36. 56 = 2 × 2 × 2 × ______
37. 63 = 3 × 3 × ______
38. 70 = 2 × 5 × ______
39. 84 = 2 × 2 × 3 × ______
40. 90 = 2 × 3 × 3 × ______

D. Choose the Correct Answer

41. What is the prime factorization of 12?
    a) 2 × 6
    b) 2 × 2 × 3
    c) 3 × 4
    d) 1 × 12
42. What is the prime factorization of 18?
    a) 2 × 3 × 3
    b) 2 × 9
    c) 3 × 6
    d) 1 × 18
43. Which number is a prime number?
    a) 21
    b) 25
    c) 29
    d) 33
44. Which is the prime factorization of 36?
    a) 2² × 3²
    b) 4 × 9
    c) 6 × 6
    d) 2 × 18
45. What is the prime factorization of 50?
    a) 2 × 5²
    b) 5 × 10
    c) 2 × 25
    d) 1 × 50
46. Which number has the prime factorization 2³ × 3?
    a) 18
    b) 24
    c) 30
    d) 36
47. Which number has the prime factorization 3² × 5?
    a) 30
    b) 45
    c) 50
    d) 75
48. The prime factors of 70 are:
    a) 2, 5, 7
    b) 2, 7, 10
    c) 5, 14
    d) 7, 10
49. Which is the prime factorization of 100?
    a) 2² × 5²
    b) 4 × 25
    c) 10 × 10
    d) 2 × 50
50. A prime factorization contains only:
    a) Even numbers
    b) Odd numbers
    c) Prime numbers
    d) Composite numbers

E. True or False

51. 2 is a prime factor of every even number. __________
52. 1 is a prime number. __________
53. 3 × 5 × 7 is the prime factorization of 105. __________
54. 2 × 2 × 3 is the prime factorization of 12. __________
55. Every composite number can be written as a product of prime numbers. __________
56. 2² × 3 = 12. __________
57. 5 × 7 = 35. __________
58. 3 × 3 × 5 = 45. __________

F. Challenge Questions

59. Find the prime factorization of 180.
60. Find the prime factorization of 210.
61. Find the prime factorization of 225.
62. Find the prime factorization of 240.
63. Find the prime factorization of 270.
64. Find the prime factorization of 300.
65. Which number is represented by 2³ × 3²?
66. Which number is represented by 2² × 5²?
67. Which number is represented by 3³ × 5?
68. Write a number whose prime factorization is 2 × 3 × 7.

Total Questions: 68

Answer Key — Prime Factorization Worksheet

A. Find the Prime Factorization

1. 12 = 2² × 3
2. 18 = 2 × 3²
3. 20 = 2² × 5
4. 24 = 2³ × 3
5. 30 = 2 × 3 × 5
6. 36 = 2² × 3²
7. 40 = 2³ × 5
8. 42 = 2 × 3 × 7
9. 45 = 3² × 5
10. 48 = 2⁴ × 3
11. 50 = 2 × 5²
12. 54 = 2 × 3³
13. 56 = 2³ × 7
14. 60 = 2² × 3 × 5
15. 63 = 3² × 7
16. 72 = 2³ × 3²
17. 75 = 3 × 5²
18. 80 = 2⁴ × 5
19. 84 = 2² × 3 × 7
20. 90 = 2 × 3² × 5

B. Use Exponents

21. 16 = 2⁴
22. 32 = 2⁵
23. 64 = 2⁶
24. 72 = 2³ × 3²
25. 100 = 2² × 5²
26. 108 = 2² × 3³
27. 120 = 2³ × 3 × 5
28. 125 = 5³
29. 144 = 2⁴ × 3²
30. 150 = 2 × 3 × 5²

C. Find the Missing Prime Factor

31. 2
32. 3
33. 2
34. 5
35. 3
36. 7
37. 7
38. 7
39. 7
40. 5

D. Choose the Correct Answer

41. b) 2 × 2 × 3
42. a) 2 × 3 × 3
43. c) 29
44. a) 2² × 3²
45. a) 2 × 5²
46. b) 24
47. b) 45
48. a) 2, 5, 7
49. a) 2² × 5²
50. c) Prime numbers

E. True or False

51. True
52. False
53. True
54. True
55. True
56. True
57. True
58. True

F. Challenge Questions

59. 180 = 2² × 3² × 5
60. 210 = 2 × 3 × 5 × 7
61. 225 = 3² × 5²
62. 240 = 2⁴ × 3 × 5
63. 270 = 2 × 3³ × 5
64. 300 = 2² × 3 × 5²
65. 2³ × 3² = 72
66. 2² × 5² = 100
67. 3³ × 5 = 135
68. 42