Math 6
Unit 1
Lesson 5
Prime and Composite Numbers
Numbers in Nature
Did you know that the number of petals on a flower is almost always from a
special set of numbers? Most often, the number of petals on a flower is one
of these numbers:
3, 5, 8, 13, 21, 34 or 55
Here are a few specific examples:
Flower
Lily
3
Buttercups
5
Chicory
Daisy
Black-eyed Susan
with 13 Petals
Math 6
Number of Petals
21
21, 34 or 55
Shasta Daisy
with 21 Petals
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Math 6
Unit 1
Lesson 5: Prime and Composite Numbers
These are special numbers from a pattern called
the Fibonacci sequence.
Leonardo da Pisa,
“Fibonacci”
1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
There are two different types of numbers in this
sequence. Some of them have only two factors:
1 and itself. Some have more factors.
Leonardo da Pisa, who lived in Italy around the
year 1200 was known as Fibonacci. He discovered
this special sequence of numbers that often appear
in nature.
Reflection
Which numbers of the Fibonacci sequence have
factors that are not limited to 1 and itself?
Objectives for this Lesson
In this lesson you will explore the following concepts:
• Provide an example of a prime number
• Provide an example of a composite number
• Sort a given set of numbers as prime and composite.
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Math 6
Unit 1
Lesson 5: Prime and Composite Numbers
Prime and Composite Numbers
You can use what you know about factors of numbers to classify whole numbers
into two categories: prime numbers, and composite numbers.
Term
Definition
Example
Prime
Number
A counting number greater than
1 that has exactly two different
whole number factors, 1 and itself.
5 = 1 x 5, and 5
has no other whole number factors
Composite
Number
A counting number with more
than two different whole number
factors greater than 1.
8=1x8
8=2x4
The factors of 8 are 1, 2, 4 and 8.
You can use these definitions to classify any whole number.
Example 1
Write all of the factors for each number. Next, identify the number as
prime or composite.
a. 12
b. 17
Factors
c. 36
d. 41
Prime or Composite?
a.
1, 2, 3, 4, 6, 12
Composite
b.
1, 17
Prime
c.
1, 2, 3, 4, 6, 9, 12, 18, 36
Composite
d.
1, 41
Prime
In order for a number to be prime, it can only be written as a product of
two unique factors.
• ONE of the two factors is 1.
• ONE of the two factors is a whole number, but is NOT 0 or 1.
Math 6
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Math 6
Unit 1
Factor
Not 1 or 0
Lesson 5: Prime and Composite Numbers
x
Factor
must be 1
=
Product
You can find factors easily enough if you know your multiplication facts.
It is a bit harder to think backward when identifying the prime numbers.
Use the following Exploration to identify all of the prime numbers up to 100.
Let’s Explore
Exploration 1: Can You Find the Primes?
Materials: Unit 1, Lesson 5, Exploration 1 page in your Workbook, A Pencil Crayon, Pencil
For 1 – 5: Use the Number Chart on the Exploration page in your Workbook.
1. Colour the 1 and circle the first four prime numbers: 2, 3, 5, 7
2. Colour the multiples of 2 but do not colour the 2.
3. Colour the multiples of 3 but do not colour the 3.
4. Colour the multiples of 5 but do not colour the 5.
5. Colour the multiples of 7 but do not colour the 7.
6.List the numbers that are circled and the numbers
that are not coloured in order.
7.These are the prime numbers up to 100. Check each number
to be sure that it has no factors other than 1 and itself.
8. Reflect: Why do you think you did not have to colour multiples of 6?
9. Reflect: Why do you think you did not have to colour multiples of 11?
10.What is the smallest prime number greater than 100? Describe how you found
that number.
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Math 6
Unit 1
Lesson 5: Prime and Composite Numbers
Let’s Practice
• Turn in your Workbook to Unit 1, Lesson 5 and complete 1 to 18.
Prime Number Factors
For each composite number greater than one you can find a unique set of two or
more prime numbers that are factors of the number. These primes will give you
a product of the number. This is called the prime factorization of a number.
Here is the prime factorization of each composite number up to 20.
Number
Prime
Factorization
4
2x2
6
2x3
8
2x2x2
9
3x3
10
2x5
12
2x2x3
14
2x7
15
3x5
16
2x2x2x2
18
2x3x3
20
2x2x5
To find the prime factorization of a number you can use a factor tree. This is a
way of reducing the number down to the primes, by using repeated division.
Math 6
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Math 6
Unit 1
Lesson 5: Prime and Composite Numbers
Example 2
Find the prime factorization of 68.
1. S
tart by dividing by
any number. Here you
see how to start with
dividing by 4:
2. N
ow look at the factors
you have so far. Can you
find any factors of 4?
If so, divide again
68
4
68
4
17
2
17
2
Now look at 17. Since 17 is prime and 2 is also prime you are finished.
The prime factorization of 68 = 2 x 2 x 17
Example 3
Which number has a prime factorization of 2 x 3 x 3 x 5?
Prime Factorization:
Multiply the numbers in order from left to right:
Now multiply 18 x 5:
Finally, the answer:
2x3x3x5
6x3x5
18 x 5
90
• Go online to complete the Concept Capsule: Prime Factorization.
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Math 6
Unit 1
Lesson 5: Prime and Composite Numbers
Let’s Practice
• Turn in your Workbook to Unit 1, Lesson 5 and complete 19 to 26.
What About 1 and 0?
The definition of a prime number leaves out 1 and 0. These are also whole
numbers. Why do you think they are not included in the prime number set?
0?
Prime: 2, 3, 5, 7, 11,…
Composite: 4, 6, 8, 9, 10,…
1?
The definition tells you that a prime number is divisible by 1 and the number
itself. It also says that they must be two different numbers.
The number 1 can be expressed as a product in many ways:
1x1
1x1x1
1x1x1x1
…and so on.
This means that by the definition of prime numbers, 1 cannot be a prime.
The number 0 can also be expressed in many ways:
0x1
0x2
0x3
…and so on.
Math 6
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Math 6
Unit 1
Lesson 5: Prime and Composite Numbers
By studying the definition you can see that 0 and 1 are not prime numbers.
Since they are not considered prime, you may think, “Why are 0 and 1 not
composite numbers?”
A composite number must be the product of two factors that are
• not the number itself.
• different from 1 and the number.
Look at 1 and 0:
1 only has one factor, not two different factors: 1 x 1 = 1
0 is not a product of two factors that are not 0. 0 is always a product of one or
more factors that include 0.
You should now be able to explain why 1 and 0 are not prime or composite.
Let’s Practice
• Turn in your Workbook to Unit 1, Lesson 5 and complete 27 to 28.
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