Chapter 2 Study Guide
Write the prime factorization for each number. List
the factors in order from least to greatest.
Write the prime factorization for each number.
Then, determine the least common multiple.
1. 30
13. 40, 100
2. 40
14. 50, 105
3. 55
4. 60
Complete each factor tree. Then write the prime
factorization for each number. List the factors in
order from least to greatest.
List the factors of each number. Then, determine
the greatest common factor.
15. 48, 20
16. 15, 16
17. 14, 28, 49
5.
Write the prime factorization for each number.
Then, determine the greatest common factor.
6.
18. 18, 42
19. 54, 45
20. 36, 60
7.
Identify the base and the exponent in each power.
Then evaluate the power.
8. 73=
9. 32=
List the multiples of each number. Then, determine
the least common multiple.
10. 6, 9
11. 4, 7
12. 4, 14, 8
Chapter 2 Study Guide
Answer Section
1. ANS:
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
2. ANS:
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
3. ANS:
55 = 5  11
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
4. ANS:
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
5. ANS:
180 = 2  2  3  3  5
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
6. ANS:
224 = 2  2  2  2  2  7
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
7. ANS:
504 = 2  2  2  3  3  7
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
8. ANS:
The base is 7 and the exponent is 3.
Sample answer: Seven cubed.
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
9. ANS:
The base is 3 and the exponent is 2.
Sample answer: Three squared.
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
10. ANS:
PTS: 1
REF: 2.1
NAT: 6.NS.4 | 6.EE.1
TOP: Skills Practice
KEY: prime factorization | Associative Property of Multiplication | factor tree | power | base | exponent |
Fundamental Theorem of Arithmetic
11. ANS:
Multiples of 6: 6, 12, 18, 24…
Multiples of 9: 9, 18, 27…
The LCM of 6 and 9 is 18.
PTS: 1
REF: 2.2
NAT: 6.NS.4
KEY: common multiple | least common multiple (LCM)
12. ANS:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32…
Multiples of 7: 7, 14, 21, 28, 35…
The LCM of 4 and 7 is 28.
TOP: Skills Practice
PTS: 1
REF: 2.2
NAT: 6.NS.4
TOP: Skills Practice
KEY: common multiple | least common multiple (LCM)
13. ANS:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60…
Multiples of 14: 14, 28, 42, 56, 70…
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64…
The LCM of 4, 14, and 8 is 56.
PTS: 1
REF: 2.2
NAT: 6.NS.4
KEY: common multiple | least common multiple (LCM)
14. ANS:
TOP: Skills Practice
The LCM of 40 and 100 is 200.
PTS: 1
REF: 2.2
NAT: 6.NS.4
KEY: common multiple | least common multiple (LCM)
15. ANS:
TOP: Skills Practice
The LCM of 50 and 105 is 1050.
PTS: 1
REF: 2.2
NAT: 6.NS.4
KEY: common multiple | least common multiple (LCM)
16. ANS:
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
TOP: Skills Practice
Factors of 20: 1, 2, 4, 5, 10, 20
The greatest common factor of 48 and 20 is 4.
PTS: 1
REF: 2.3
NAT: 6.NS.4
TOP: Skills Practice
KEY: common factor | greatest common factor (GCF) | relatively prime numbers
17. ANS:
Factors of 15: 1, 3, 5, 15
Factors of 16: 1, 2, 4, 8, 16
The greatest common factor of 15 and 16 is 1. The numbers are relatively prime numbers.
PTS: 1
REF: 2.3
NAT: 6.NS.4
TOP: Skills Practice
KEY: common factor | greatest common factor (GCF) | relatively prime numbers
18. ANS:
Factors of 14: 1, 2, 7, 14
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 49: 1, 7, 49
The greatest common factor of 14, 28, and 49 is 7.
PTS: 1
REF: 2.3
NAT: 6.NS.4
TOP: Skills Practice
KEY: common factor | greatest common factor (GCF) | relatively prime numbers
19. ANS:
The GCF of 18 and 42 is 6.
PTS: 1
REF: 2.3
NAT: 6.NS.4
TOP: Skills Practice
KEY: common factor | greatest common factor (GCF) | relatively prime numbers
20. ANS:
The GCF of 54 and 45 is 9.
PTS: 1
REF: 2.3
NAT: 6.NS.4
TOP: Skills Practice
KEY: common factor | greatest common factor (GCF) | relatively prime numbers
21. ANS:
The GCF of 36 and 60 is 12.
PTS: 1
REF: 2.3
NAT: 6.NS.4
TOP: Skills Practice
KEY: common factor | greatest common factor (GCF) | relatively prime numbers