Prime and Composite Numbers
Name
7.2
?
Prime and Composite Numbers
Essential Question
Algebraic Reasoning—5.4.A MATHEMATICAL PROCESSES 5.1.A, 5.1.D
How can you tell whether a number is prime or composite?
Unlock Unlock the the Problem Problem Students are arranging square tables to make one larger, rectangular table at a fundraiser for an animal shelter. If the students want to choose from the greatest number of ways to arrange the tables, should they use 12 or 13 square tables?
• What are the factors of 12?
Use a grid to show all the possible arrangements of 12 and 13 tables. Label each drawing with the factors modeled.
ERROR Alert
The same factors in a different order should be counted only once. For example, 3 × 4 and 4 × 3 are the same factor pair.
Math Talk Mathematical Processes
So, there are more ways to arrange _ tables.
Explain how knowing whether 12 and 13 are prime or composite could have helped you solve the problem above.
• A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself.
© Houghton Mifflin Harcourt Publishing Company
• A composite number is a whole number greater than 1 that has more than two factors. Factors of 12: _ , _ , _ , _ , _ , _ Factors of 13: _ , _ 12 is a __ number, and 13 is a __ number.
Module 7
297
Divisibility You can use divisibility rules to help tell whether a number is prime or composite. If a number is divisible by any number other than 1 and itself, then the number is composite.
Math Idea The number 1 is neither prime nor composite, since it has only one factor: 1.
Tell whether 51 is prime or composite. Is 51 divisible by 2? Is 51 divisible by 3? Think: 51 is divisible by a number other than 1 and 51. 51 has more than two factors.
So, 51 is ___ .
Share Share and and Show Show Tell whether the number is prime or composite. 1. 11 Think: Does 11 have
2. 73
3. 69
4. 42
other factors besides 1 and itself?
Math Talk
Problem Problem Solving Solving
Mathematical Processes
Analyze Write true or false for each statement.
Is the product of two prime numbers prime or composite? Explain.
5. The number 1 is not prime.
6. A composite number cannot have three factors.
7. Only odd numbers are prime numbers.
8. Every multiple of 7 is a composite number.
9.
298
Name a 2-digit odd number that is prime. Name a 2-digit odd number that is composite.
© Houghton Mifflin Harcourt Publishing Company
Explain or give an example to support your answer.
Name
Problem Problem Solving Solving Eratosthenes was a Greek mathematician who lived more than 2,200 years ago. He invented a method of finding prime numbers, which is now called the Sieve of Eratosthenes. 10. Multi-Step Follow the steps below to circle all prime numbers
less than 100. Then list the prime numbers. STEP 1
STEP 2
STEP 3
STEP 4
Cross out 1, since 1 is not prime.
Circle 2, since it is prime. Cross out all other multiples of 2.
Circle the next number that is not crossed out. This number is prime. Cross out all the multiples of this number.
Repeat Step 3 until every number is either circled or crossed out.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
© Houghton Mifflin Harcourt Publishing Company
11.
So, the prime numbers less than 100 are
Explain why the multiples of any number other than 1 are not prime numbers.
Module 7 • Lesson 2
299
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble completely to show your answer. 12. Reasoning Talia’s locker combination consists of three prime numbers.
The sum of these numbers is also a prime number. Which of these might be her combination?
A
3 - - 8 - - 17
B
2 - - 3 - - 19
C
7 - - 13 - - 3
D
11 - - 2 - - 5
13. A certain number is a whole number. If the number is also composite,
what must be true about the number?
A
It is odd.
B
It has more than two factors.
C
It has exactly two factors.
D
It has two or more digits.
14. Multi-Step The sum of three prime numbers is 12. What could the
numbers be?
A
3, 7, 2
B
6, 6, 0
C
3, 5, 7
D
3, 4, 5
TEXAS Test Prep
300
A
prime.
B
composite.
C
neither prime nor composite.
D
both prime and composite.
© Houghton Mifflin Harcourt Publishing Company
15. The number 2 is
Algebraic Reasoning—5.4.A MATHEMATICAL PROCESSES 5.1.A, 5.1.D
H o mewo rk and Practice
7.2
Name
Prime and Composite Numbers
Tell whether the number is prime or composite. 1. 19
2. 81
3. 52
4. 23
5. 33
6. 60
7. 31
8. 25
Write true or false for each statement. Explain or give an example to support your answer. 9. A prime number is always greater than 1.
11. Every multiple of 5 is a composite number.
10. The number 17 is a prime number.
12. A number can be both prime and composite.
Problem Solving
Problem Problem Solving Solving 13. The students in math class use square tiles to make arrays. Celia says
© Houghton Mifflin Harcourt Publishing Company
they can make more arrays with 8 tiles than with 9 tiles because 8 has more factors. Is Celia correct? Explain.
Module 7 • Lesson 2 301
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer.
football jerseys. Parker has the number 55. Nick has 47. Marshall has 16, and Leon has 9. Whose jersey has a prime number?
times this morning. In each game, the number of points she scored was a prime number. When she adds the points for the three games together, the sum is also a prime number. Which of these might be her scores?
A
Parker
B
Nick
A
17, 19, 20
C
Marshall
B
11, 17, 21
D
Leon
C
21, 23, 13
D
29, 19, 23
16. Esteban made a list of prime numbers less
than 40. He listed the numbers in order from least to greatest. Which number did Esteban put on his list after 29?
A
41
B
23
C
33
D
31
18. Multi-Step Trisha spins a spinner. The
pointer lands on three prime numbers. She says the sum is less than 12. Which could be the numbers?
302
15. Harlan played her favorite game app three
A
2, 3, 5
B
2, 4, 5
C
2, 7, 3
D
0, 9, 1
17. Carolyn found that the difference between two
prime numbers is a composite number. Which could be the prime numbers?
A
2, 5
B
13, 2
C
23, 19
D
13, 11
19. Multi-Step Felix found the sum of two prime
numbers and one composite number to be 45. The difference between the greatest and least number is 4. Which could be the three numbers?
A
13, 17, 15
B
18, 14, 13
C
15, 14, 16
D
11, 19, 12
© Houghton Mifflin Harcourt Publishing Company
14. Four boys compare the numbers on their
7.2
?
Prime and Composite Numbers
Essential Question
Algebraic Reasoning—5.4.A MATHEMATICAL PROCESSES 5.1.A, 5.1.D
How can you tell whether a number is prime or composite?
Unlock Unlock the the Problem Problem Students are arranging square tables to make one larger, rectangular table at a fundraiser for an animal shelter. If the students want to choose from the greatest number of ways to arrange the tables, should they use 12 or 13 square tables?
• What are the factors of 12?
Use a grid to show all the possible arrangements of 12 and 13 tables. Label each drawing with the factors modeled.
ERROR Alert
The same factors in a different order should be counted only once. For example, 3 × 4 and 4 × 3 are the same factor pair.
Math Talk Mathematical Processes
So, there are more ways to arrange _ tables.
Explain how knowing whether 12 and 13 are prime or composite could have helped you solve the problem above.
• A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself.
© Houghton Mifflin Harcourt Publishing Company
• A composite number is a whole number greater than 1 that has more than two factors. Factors of 12: _ , _ , _ , _ , _ , _ Factors of 13: _ , _ 12 is a __ number, and 13 is a __ number.
Module 7
297
Divisibility You can use divisibility rules to help tell whether a number is prime or composite. If a number is divisible by any number other than 1 and itself, then the number is composite.
Math Idea The number 1 is neither prime nor composite, since it has only one factor: 1.
Tell whether 51 is prime or composite. Is 51 divisible by 2? Is 51 divisible by 3? Think: 51 is divisible by a number other than 1 and 51. 51 has more than two factors.
So, 51 is ___ .
Share Share and and Show Show Tell whether the number is prime or composite. 1. 11 Think: Does 11 have
2. 73
3. 69
4. 42
other factors besides 1 and itself?
Math Talk
Problem Problem Solving Solving
Mathematical Processes
Analyze Write true or false for each statement.
Is the product of two prime numbers prime or composite? Explain.
5. The number 1 is not prime.
6. A composite number cannot have three factors.
7. Only odd numbers are prime numbers.
8. Every multiple of 7 is a composite number.
9.
298
Name a 2-digit odd number that is prime. Name a 2-digit odd number that is composite.
© Houghton Mifflin Harcourt Publishing Company
Explain or give an example to support your answer.
Name
Problem Problem Solving Solving Eratosthenes was a Greek mathematician who lived more than 2,200 years ago. He invented a method of finding prime numbers, which is now called the Sieve of Eratosthenes. 10. Multi-Step Follow the steps below to circle all prime numbers
less than 100. Then list the prime numbers. STEP 1
STEP 2
STEP 3
STEP 4
Cross out 1, since 1 is not prime.
Circle 2, since it is prime. Cross out all other multiples of 2.
Circle the next number that is not crossed out. This number is prime. Cross out all the multiples of this number.
Repeat Step 3 until every number is either circled or crossed out.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
© Houghton Mifflin Harcourt Publishing Company
11.
So, the prime numbers less than 100 are
Explain why the multiples of any number other than 1 are not prime numbers.
Module 7 • Lesson 2
299
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble completely to show your answer. 12. Reasoning Talia’s locker combination consists of three prime numbers.
The sum of these numbers is also a prime number. Which of these might be her combination?
A
3 - - 8 - - 17
B
2 - - 3 - - 19
C
7 - - 13 - - 3
D
11 - - 2 - - 5
13. A certain number is a whole number. If the number is also composite,
what must be true about the number?
A
It is odd.
B
It has more than two factors.
C
It has exactly two factors.
D
It has two or more digits.
14. Multi-Step The sum of three prime numbers is 12. What could the
numbers be?
A
3, 7, 2
B
6, 6, 0
C
3, 5, 7
D
3, 4, 5
TEXAS Test Prep
300
A
prime.
B
composite.
C
neither prime nor composite.
D
both prime and composite.
© Houghton Mifflin Harcourt Publishing Company
15. The number 2 is
Algebraic Reasoning—5.4.A MATHEMATICAL PROCESSES 5.1.A, 5.1.D
H o mewo rk and Practice
7.2
Name
Prime and Composite Numbers
Tell whether the number is prime or composite. 1. 19
2. 81
3. 52
4. 23
5. 33
6. 60
7. 31
8. 25
Write true or false for each statement. Explain or give an example to support your answer. 9. A prime number is always greater than 1.
11. Every multiple of 5 is a composite number.
10. The number 17 is a prime number.
12. A number can be both prime and composite.
Problem Solving
Problem Problem Solving Solving 13. The students in math class use square tiles to make arrays. Celia says
© Houghton Mifflin Harcourt Publishing Company
they can make more arrays with 8 tiles than with 9 tiles because 8 has more factors. Is Celia correct? Explain.
Module 7 • Lesson 2 301
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer.
football jerseys. Parker has the number 55. Nick has 47. Marshall has 16, and Leon has 9. Whose jersey has a prime number?
times this morning. In each game, the number of points she scored was a prime number. When she adds the points for the three games together, the sum is also a prime number. Which of these might be her scores?
A
Parker
B
Nick
A
17, 19, 20
C
Marshall
B
11, 17, 21
D
Leon
C
21, 23, 13
D
29, 19, 23
16. Esteban made a list of prime numbers less
than 40. He listed the numbers in order from least to greatest. Which number did Esteban put on his list after 29?
A
41
B
23
C
33
D
31
18. Multi-Step Trisha spins a spinner. The
pointer lands on three prime numbers. She says the sum is less than 12. Which could be the numbers?
302
15. Harlan played her favorite game app three
A
2, 3, 5
B
2, 4, 5
C
2, 7, 3
D
0, 9, 1
17. Carolyn found that the difference between two
prime numbers is a composite number. Which could be the prime numbers?
A
2, 5
B
13, 2
C
23, 19
D
13, 11
19. Multi-Step Felix found the sum of two prime
numbers and one composite number to be 45. The difference between the greatest and least number is 4. Which could be the three numbers?
A
13, 17, 15
B
18, 14, 13
C
15, 14, 16
D
11, 19, 12
© Houghton Mifflin Harcourt Publishing Company
14. Four boys compare the numbers on their
