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Date
Class
Practice C
2-4 Prime Factorization
Use a factor tree to find the prime factorization.
1. 84
2. 343
3. 135
4. 180
5. 48
6. 225
7. 93
8. 126
Use a step diagram to find the prime factorization.
9. 290
10. 900
11. 575
12. 90
13. 220
14. 350
15. 495
16. 480
17. 2,000
18. 1,040
19. 1,650
20. 3,000
21. The prime factorization of a number is 22 • 35. What is
the number?
22. You can factor 150 as 15 • 10. List four other ways can you
factor 150.
23. A number x is a prime factor of 65 and 104. What is the number?
Write the composite number for each prime factorization.
24. 25 • 52
25. 33 • 5 • 11
26. 43 • 7 • 13
27. 28 • 35
28. The prime factors of a number are all the prime numbers
between 20 and 30. No factor is repeated. What is the number?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
39
Holt Middle School Math Course 2
Practice C
2-4 Prime Factorization
Practice B
2-4 Prime Factorization
LESSON
LESSON
Use a factor tree to find the prime factorization.
Use a factor tree to find the prime factorization.
1. 57
2. 49
3. 88
2
3 • 19
3
7
5. 105
2 • 11
6. 98
9. 68
10. 91
2
2 • 17
7 • 13
13. 189
2 •3•5
14. 270
33 • 7
2 • 33 • 5
33 • 72
18. 144
23 • 7
24 • 32
21. 124
22. 515
22 • 31
25. 126
26. 104
2
2•3 •7
2 • 13
29. 450
2 • 32 • 52
13
52 • 7
31. 1,040
23 • 53
23. A number x is a prime factor of 65 and 104. What is the number?
28. 175
2 • 3 • 11
30. 1,000
5 • 30; 3 • 50; 6 • 25; 2 • 75
22 • 5 • 11
27. 66
3
22. You can factor 150 as 15 • 10. List four other ways can you
factor 150.
24. 220
52 • 29
5 • 103
Write the composite number for each prime factorization.
32. 2,500
24 • 5 • 13
23 • 3 • 53
5
972
23 • 3 • 7
23. 725
20. 3,000
2 • 3 • 52 • 11
21. The prime factorization of a number is 2 • 3 . What is
the number?
20. 168
2 • 5 • 37
25 • 3 • 5
19. 1,650
24 • 5 • 13
2
19. 370
16. 480
32 • 5 • 11
18. 1,040
24 • 53
2 • 32 • 5
15. 495
2 • 52 • 7
17. 2,000
12. 90
52 • 23
14. 350
22 • 5 • 11
Use a step diagram to find the prime factorization.
17. 56
2 • 32 • 7
11. 575
22 • 32 • 52
13. 220
16. 1,323
22 • 5 • 7
8. 126
3 • 31
10. 900
2 • 5 • 29
2
2 •3
15. 140
7. 93
32 • 52
9. 290
3
22 • 32 • 5
Use a step diagram to find the prime factorization.
12. 72
2
4. 180
33 • 5
6. 225
24 • 3
2•3•7
11. 60
3. 135
73
5. 48
8. 42
22 • 13
2. 343
22 • 3 • 7
5 • 19
7. 52
2 • 72
3•5•7
1. 84
4. 95
24. 25 • 52
22 • 54
25. 33 • 5 • 11
26. 43 • 7 • 13
1,485
5,824
800
2
33. The prime factorization of a number is 3 • 5 • 11. What is
the number?
27. 28 • 35
62,208
28. The prime factors of a number are all the prime numbers
between 20 and 30. No factor is repeated. What is the number?
495
667
38
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Middle School Math Course 2
Reteach
2-4 Prime Factorization
Challenge
2-4 A Different Point of View
To write the prime factorization of a number, write the number as
the product of only prime numbers. A prime number has only two
factors, itself and 1.
Use a factor tree to find the prime
factorization of 18.
18
2
Create two more factor trees with different factors for
each number. Possible answers are given.
1.
225
Use a factor tree to find the prime
factorization of 36.
25
5
36
Keep factoring until all
the factors are prime.
3
4
3
2
225
5
3
2
3
3
504
2
2
168
4
4. 63
32 • 52
504
3
Use a factor tree to find the prime factorization.
3
21
2
7
504
2
2 •5
3
2 •7
2•3
3 •7
84
12 7
3
4
2
Prime factorization of 504:
1) The divisors must be prime numbers.
2) Keep dividing until the quotient is 1.
3) The divisors are the factors in the
prime factorization.
The prime factorization of 60 is
2 • 2 • 3 • 5, or 22 • 3 • 5.
2
63
4 7
2
2 3
9
3
3
2
23 • 32 • 7
3. In 1742, Christian Goldbach wrote his now famous Goldbach’s
Conjecture, which states that every even number greater than 2
can be represented as the sum of 2 primes. Although this
conjecture is still an open question, it can be supported. Choose
3 even numbers greater than 2 to help support Goldbach’s
Conjecture.
Use a step diagram to find the prime
factorization of 75.
Use a step diagram to find the prime
factorization of 60.
2|60
2|30
3|15
5|5
1
2
8
252
2
2
5 9
3 3
8
3. 54
5
45
3 5 3 5
3
Prime factorization of 225:
The prime factorization of 36 is
2 • 2 • 3 • 3, or 22 • 32.
2. 28
225
15
15
9
9
2.
The prime factorization of 18 is
2 • 3 • 3, or 2 • 32.
1. 20
Holt Middle School Math Course 2
LESSON
LESSON
6
39
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
3|75
5|25
5|5
1
Possible answer: 12 ! 7 " 5; 32 ! 19 " 13; 44 ! 13 " 31
The prime factorization of 75 is
3 • 5 • 5, or 3 • 52.
4. Goldbach also made a conjecture that every odd number is the
sum of 3 primes. Choose 3 odd numbers to support this conjecture.
Possible answer: 13 ! 3 " 5 " 5; 15 ! 5 " 5 " 5; 33 ! 23 " 5 " 5
Use a step diagram to find the prime factorization.
5. 48
6. 24
24 • 3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
7. 40
23 • 3
8. 98
23 • 5
40
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
2 • 72
Holt Middle School Math Course 2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
137
41
Holt Middle School Math Course 2
Holt Middle School Math Course 2