Unit 1 Lesson 1: Prime or Composite?
In this lesson you will:
 Determine if a number is prime or composite
 Know how prime and composite numbers relate to reducing and factoring
numbers and equations
Rules:
- A prime number is a natural number greater than 1 that has only two factors, itself
and 1.
- A composite number is a natural number that more than one set of factors
It's a really good idea to be able to figure out if a number is prime or composite. Why?
When working out math problems you should be able to determine if you have reduced
the answer to its simplest terms. To do this you need to identify if a number is prime or
composite. This becomes more important when factoring polynomials.
In ancient Greece, a mathematician called Eratosthenes (c. 276 BC - c. 195 BC) came up
with a method of finding prime numbers. This method is called The Sieve of Eratosthenes:
You start by making a grid of the numbers 1
– 100
First, cross out 1, since it isn't prime:
Next, move to # 2... It's prime, so circle it and go through the entire list and cross out all
numbers that 2 goes into. These numbers are composite.
Now, move to #3
If it hasn't been crossed out yet, it's prime! Circle it and then go through and cross
out all the numbers that 3 goes into (which is every third number). These numbers
are composite.
Can you figure out how this goes from here? Review the examples and complete the
practice problems. This is a good strategy to use when learning about composite
numbers and factors.
Example #1: Classify 29 as a prime or composite number.
Answer: ‘P’ =Prime
Factors of 29 are 1 and itself (29) only.
Example #2: Classify 8 as prime or composite number.
Answer: ‘C’ = Composite
Factors of 8 are 1,2,4,8.
Example #3: Classify the 17 as a prime or composite number.
Answer: ‘P’ = Prime
Factors of 17 are 1 and itself (17) only.
Example #4: Classify the number 15 as a prime or composite number.
Answer: ‘C’ = Composite
Factors of 15 are 1, 3, 5, 15.
Practice Problems: Prime or Composite Numbers
Classify each number as prime or composite. If the number is ‘prime’ then write ‘P’ for
prime and then list the set of prime factors. If the number is composite write ‘C’ for
composite and list all factors of the number.
1. 11
2. 20
3. 9
4. 55
5. 88
6. 61
7. 31
8. 8
9. 13
10. 3
11. 83
12. 5
Research questions:
13. Explain why the number 2 the only even prime.
14. Conduct research to identify at least four different ‘divisibility rules’ that help you
determine if one number is divisible by another certain number. For example, what
divisibility rule will help you determine if a number is divisible by 10? List the rules that
you identified in your research. Provide an example for each rule.
Submit your answers in the text box.