Download The Think Tank Vocabulary

Lesson 2.1 Skills Practice
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The Think Tank
Prime Factorization and Factor Trees
Vocabulary
Match each definition to its corresponding term.
1. A diagram that uses branches to show how
a. Associative Property
a number can be written as the product of of Multiplication
prime numbers.
2. The expression of a composite number as b. base
a product of prime numbers.
3. An expression that represents repeated multiplication of a factor. 4. The factor that is repeatedly multiplied c. Fundamental
Theorem of Arithmetic
d. prime factorization
in a power.
5. A property that states that changing the e. exponent
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grouping of the factors in a multiplication
statement does not change the product.
6. The number of times a base is used as a f. factor tree
factor of repeated multiplication.
7. A theorem that states that every natural g. power
number is either prime or can be uniquely
written as a product of primes.
Chapter 2 Skills Practice • 335
Lesson 2.1 Skills Practice
page 2
Problem Set
Write the prime factorization for each number. List the factors in order from least to greatest.
1. 12
2. 30
12 5 2 3 6
523233
3. 24
5. 40
7. 55
8. 36
9. 60
6. 27
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10. 20
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4. 18
Lesson 2.1 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
Rewrite each set of factors using the Associative Property of Multiplication.
Show that the original grouping and the new grouping are equivalent.
11. (2 3 3) 3 4 5 2 3 (3 3 4)
12. (2 3 2) 3 5 5
(2 3 3) 3 4 5 2 3 (3 3 4)
6 3 4 5 2 3 12
24 5 24
14. 4 3 (2 3 6) 5
15. (2 3 2) 3 (4 3 3) 5
16. (3 3 2) 3 (5 3 2) 5
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13. 3 3 (5 3 3) 5
Chapter 2 Skills Practice • 337
Lesson 2.1 Skills Practice
page 4
Complete each factor tree. Then write the prime factorization for each number. List the factors
in order from least to greatest.
180
17.
6
2
3
30
3
135
18.
2
45
15
3
5
180 5 2 3 2 3 3 3 3 3 5
19.
20.
224
8
630
63
28
10
945
21.
22.
9
9
105
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504
Lesson 2.1 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
Identify the base and the exponent in each power. Then write each power in words.
23. 52
24. 73
The base is 5 and the exponent is 2.
Sample answer: Five squared.
26. 32
27. 29
28. 83
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25. 45
Chapter 2 Skills Practice • 339
Lesson 2.1 Skills Practice
page 6
Complete each factor tree. Then write the prime factorization for each number.
List the factors in order from least to greatest using powers.
29.
30.
216
8
2
27
4
3
2
2
252
9
28
9
3
3
216 5 2 3 2 3 2 3 3 3 3 3 3
5 23  33
31.
32.
588
12
34.
72
8
27
25
49
33.
675
9
340 • Chapter 2 Skills Practice
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18
21
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