# 1.03 Prime and composite numbers

Lesson

## Ideas

When we looked at  factors of numbers  , we found that some numbers only had themselves and 1 as factors, while others have more factors. Try this problem to review finding the factors of a number.

### Exploration

Drag the sliders to find multiples of numbers from 1 to 12.

The number sentence shows us multiples of the numbers on the left, and factors of the number on the right. e.g. 6\times 8=48 means that 6 and 8 are factors of 48, and that 48 is a multiple of 6 and of 8.

### Examples

#### Example 1

Which of these numbers is 6 a factor of?

A
30
B
32
C
17
D
39
Worked Solution
Create a strategy

Write down the multiples of 6.

Apply the idea

The first 7 multiples of 6 are: 6,\, 12,\, 18,\, 24,\, 30,\, 36,\, 42.

Out of all the options only 30 is in the above list.

The correct answer is Option A.

Idea summary

6\times 8=48 means that 6 and 8 are factors of 48, and that 48 is a multiple of 6 and of 8.

## Prime and composite numbers

What are prime and composite numbers? How can we determine if a number is prime or composite? Let's take a look and see.

### Examples

#### Example 2

True or False? 40 is a composite number.

Worked Solution
Create a strategy

Find the factors of 40.

Apply the idea

The factors of 40 are 1,2,4,5,8,10,20,40.

Since 40 has more than 2 factors, then it is a composite number. This means the statement is true.

#### Example 3

True or False? 79 is a prime number.

Worked Solution
Create a strategy

Find the factors of 79.

Apply the idea

The factors of 79 are 1 and 79.

Since 79 is only divisible by 1 and itself, then it is a prime number. This means the statement is true.

Idea summary
• Every whole number greater than 1 is either a prime number or a composite number

• All even numbers greater than 2 are composite numbers

• To be a prime number, a number can only have itself and 1 as factors

• 0 and 1 are not prime or composite numbers

### Outcomes

#### MA3-4NA

orders, reads and represents integers of any size and describes properties of whole numbers