# 1.04 Square and triangular numbers

Lesson

## Ideas

We've seen that  prime and composite numbers  are two types of numbers that can help us with calculations.

### Examples

#### Example 1

The only factors a prime number has is 1 and itself.

Which of the following numbers are prime?

A
10
B
21
C
19
Worked Solution
Create a strategy

Write the factors of each option.

Apply the idea

Option A: 10 has the following factors:1,2,5,10

Option B: 21 has the following factors:1,3,7,21

Option C: 19 has the following factors:1,19

Among the choices, 19 is a prime number as its factors are 1 and itself. So, the correct answer is Option C.

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

## Square numbers

### Examples

#### Example 2

Write down the next square number after 16.

Worked Solution
Create a strategy

Find the 5th square number.

Apply the idea

16 is the 4th square number since 4\times 4=16.

To find the square number after 16, we need to find the 5th square number which is:5\times 5=25

25 is the next square number after 16.

Idea summary

If we multiply a number by itself, we make a square number. If we use dots to picture this as an array it will make a square shape.

## Triangular numbers

### Examples

#### Example 3

Write down the next 3 triangular numbers.1,\,3,\,6,\,10,\,15,\,⬚,\,⬚,\,⬚

Worked Solution
Create a strategy

Add the the position of the number we are finding to the previous triangular number.

Apply the idea

To find the 6th triangular number we add 6 to the previous triangular number of 15:

To find the 7th triangular number we add 7 to the previous triangular number of 21:

To find the 8th triangular number we add 8 to the previous triangular number of 28:

Here is the complete list of triangular numbers:1,\,3,\,6,\,10,\,15,\,21,\,28,\,36

Idea summary

With triangular numbers, we add 1 more dot to each new row and create a triangle shape with dots.

### Outcomes

#### MA3-4NA

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