
Prime and Composite
Numbers 

Unit 3
> Lesson 3 of 9 
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. Select your answer by clicking on its button. Feedback to your answer
is provided in the RESULTS BOX. If you make a mistake, choose a different button.

1.

Each of the following numbers is composite EXCEPT:
30, 31, 32, 33, 34, 35, 36, 37, 38, 39

2.

The prime numbers between 40 and 49 are:

3.

The prime numbers between 50 and 59 are:

4.

The prime numbers between 60 and 69 are:

5.

The prime numbers between 20 and 69 are:

This lesson is by Gisele Glosser. You can find me on Google.
