Lesson 2 — Activity 3: Composites and Prime Factorizations


Getting Ready


In the previous two activities, you have practised finding multiples and factors. Take a moment to think once more what each of these are.


For the number 6:


The first five multiples of 6 are:


  • 6 x 1 = 6
  • 6 x 2 = 12
  • 6 x 3 = 18
  • 6 x 4 = 24
  • 6 x 5 = 30


  • 6: {6, 12, 18, 24, 30}


You will use your knowledge of multiples and factors in this activity.
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The factors of 6 are:


  • 6 ÷ 1 = 6
  • 6 ÷ 2 = 3
  • 6 ÷ 3 = 2


  • 6: {1, 2, 3, 6}


           In this activity, you will learn about prime and composite numbers.

In this activity, you will learn about the types of numbers.

There are two types of numbers:


Prime numbers:


  • A prime number is a number that can only be divided by itself and 1. Another way to think of prime numbers is that they only have 2 factors. O and 1 are not prime numbers.


  • The first five prime numbers are 2, 3, 5, 7, and 11.

Composite numbers:


  • A composite number is a number that can be divided by more than itself and 1 (meaning they have more than two factors).


  • 4 is the first composite number because it can be divided by 1, 2, and 4


Try This:



Is the number 14 a prime or a composite number?




14 is a composite number because it can be divided by more than itself and 1. It can be divided by 1, 2, 7, and 14.




Prime numbers are the building blocks of all other numbers. We can break down any number into the prime numbers that can be multiplied to create it. There is only one set of prime numbers that can be used to create any number!


When we find two prime numbers that multiply together to make a composite number, we call this prime factorization.

For example, the number 10 is a composite number, but if we look at the factors 2 and 5, we realize they are both prime numbers, so we can show this as

10 = 2 x 5

That’s prime factorization.

Prime factorization is finding which prime numbers you need to multiply together to get the original number.


Let's look at the number 12. What are the prime factors of 12?
It is best to start working from the smallest prime number, which is 2, so let's check:

12 ÷ 2 = 6

But 6 is not a prime number, so we need to factor it further:

6 ÷ 2 = 3

And 3 is a prime number, so:

12 = 2 x 2 x 3

As you can see, every factor is a prime number, so the answer must be right.

The prime factorization of 12 is 2 x 2 x 3.


Let's try another one. Let's look at the number 24.

24÷ 2 = 12

12 is not a prime number, so factor further.

12 ÷ 2 = 6

6 is not a prime number, so factor further:

6 ÷ 2 = 3

And 3 is a prime number so:

The prime factorization of 24 is 3 x 2 x 2 x 2.

What about 9?

2 does not divide evenly into 9, so start with 3:

9 ÷ 3 = 3

Because 3 is a prime number, we can't do anything else.

The prime factorization of 9 is 3 x 3.

Image courtesy of www.imagesgoogle.com

Go to the next page to try a Self-check Activity to identify prime and composite numbers.