6R Prime and
Composite
Numbers 
Name ______________________ # _____

Problem 1: 
The area of a rectangular garden is 7 square yards. List all
possible wholenumber dimensions the garden can have. 

Solution: 
1 yd x 7 yd 
The wholenumber dimensions, 1 and 7, of the rectangular garden
above, are the
factors of the number 7. 
Problem 2: 
The area of a rectangular garden is 8 square yards. List all
possible wholenumber dimensions the garden can have. 




Solution: 
1 yd x 8 yd, 2 yd x 4 yd

The wholenumber dimensions, 1, 2, 4 and 8, of the rectangular
gardens in Problem 2, are the factors of the number 8. In
Problem 1, the number 7 has only two factors. The number 7 is
prime. In problem 2 above, the number 8 has four factors.
The number 8 is composite. 
Definitions
 A
prime number has only two factors: 1 and itself.
 A
composite number has more than two factors.

The number 1 is neither prime nor composite.
When the area of a rectangle is a prime number, there is only
one set of possible dimensions for that rectangle. When the area
of a rectangle is a composite number, there are two or more sets
of possible dimensions for that rectangle. Each set of
dimensions is a pair of factors.

To determine if a number is prime or composite, follow these steps:
 Find all factors of the number.
 If the number has only two factors, 1 and itself, then it is
prime.
 If the number has more than two factors, then it is composite.
Example 1: 
Is the number 2 prime or composite? 
Solution: 
The factors of 2 are 1 x 2 

2 is prime 
Example 2: 
Is the number 9 prime or composite? 
Solution: 
The factors of 9 are 1 x 9, 3 x 3 

9 is composite 
We have determined if a single number is prime or composite.
Let's look at a range of numbers to see if they are prime or
composite. Please note that each range of numbers given in
Examples 3, 4 and 5 below are
inclusive.

Example 3: 
Find all prime numbers between 2 and 9. 


factors of 2: 
1 x 2 
2 is prime 

factors of 3: 
1 x 3 
3 is prime 

factors of 4: 
1 x 4, 2 x 2 
4 is composite 

factors of 5: 
1 x 5 
5 is prime 

factors of 6: 
1 x 6, 2 x 3 
6 is composite 

factors of 7: 
1 x 7 
7 is prime 

factors of 8: 
1 x 8, 2 x 4 
8 is composite 

factors of 9: 
1 x 9, 3 x 3 
9 is composite 

Solution: 
The prime numbers between 2 and 9 are 2, 3, 5 and 7.

Example 4: 
Find all prime numbers between 10 and 19. 


factors of 10: 
1 x 10, 2 x 5 
10 is composite 

factors of 11: 
1 x 11 
11 is prime 

factors of 12: 
1 x 12, 2 x 6, 3 x 4 
12 is composite 

factors of 13: 
1 x 13 
13 is prime 

factors of 14: 
1 x 14, 2 x 7 
14 is composite 

factors of 15: 
1 x 15, 3 x 5 
15 is composite 

factors of 16 
1 x 16, 4 x 4 
16 is composite 

factors of 17: 
1 x 17 
17 is prime 

factors of 18: 
1 x 18, 3 x 6 
18 is composite 

factors of 19: 
1 x 19 
19 is prime 

Solution: 
The prime numbers between 10 and 19 are 11, 13, 17 and 19.

Example 5: 
Find all prime numbers between 20 and 29. 


factors of 20: 
1 x 20, 2 x 10, 4 x 5 
20 is composite 

factors of 21: 
1 x 21, 3 x 7 
21 is composite 

factors of 22: 
1 x 22, 2 x 11 
22 is composite 

factors of 23: 
1 x 23 
23 is prime 

factors of 24: 
1 x 24, 2 x 12, 3 x 8, 4 x 6 
24 is composite 

factors of 25: 
1 x 25, 5 x 5 
25 is composite 

factors of 26: 
1 x 26, 2 x 13 
26 is composite 

factors of 27: 
1 x 27, 3 x 9 
27 is composite 

factors of 28: 
1 x 28, 2 x 14, 4 x 7 
28 is composite 

factors of 29: 
1 x 29 
29 is prime 

Solution: 
The prime numbers between 20 and 29 are 23 and 29.

Example 6: 
Is the number 31 prime or composite? Explain your answer using
full sentences. 

Solution 1: 
The number 31 is prime because its only factors are one and
itself. 
Solution 2: 
Thirtyone is a prime number. This is because the number 31 has
only two factors: 1 and 31. 
Solution 3: 
I divided the number 31 by all numbers between 1 and 31 and
found no factors other than one and thirtyone. Therefore, 31 is
prime.

There are many possible ways to explain the solution to this problem.
These are just three possible explanations.
Summary: 
A prime number has only two factors: 1 and itself. A composite
number has more than two factors. The number 1 is neither prime
nor composite.


The prime numbers between 2 and 31 are 2, 3, 5, 7, 11, 13, 17,
19, 23, 29 and 31 since each of these numbers has only two
factors, itself and 1. 
Exercises
Directions: Read each question below. circle your answer. 
1.
Each of the following numbers is composite EXCEPT:
30, 31, 32, 33, 34, 35, 36, 37, 38, 39
32
and 39
30
and 34
31
and 37
All
composite
2.
The prime numbers between 40 and 49 are:
42,
43 and 47
41,
43 and 47
43,
45 and 47
None
of the above.
3.
The prime numbers between 50 and 59 are:
53
and 59
51
and 59
53
and 57
None
of the above.
4.
The prime numbers between 60 and 69 are:
63
and 69
61
and 67
60
and 65
None
of the above.
5.
The prime numbers between 20 and 69 are:
21,
23, 29, 31, 37, 41, 43, 47, 53, 63 and 69
23,
29, 31, 33, 37, 41, 43, 47, 59, 61 and 67
23,
29, 31, 37, 41, 43, 47, 53, 59, 61 and 67
None
of the above.
