Composite numbers in the multiplication grid

Quick answer

Composite numbers in the multiplication grid are numbers that have more than two different factor pairs. When you look at the multiplication grid, composite numbers show up in many places because they can be made by multiplying different combinations of numbers together.

Learning outcome

By the end of this page, you will understand how to find composite numbers using the multiplication grid and see why they have more than one way to be made by multiplying two numbers.

• You can spot composite numbers in the multiplication grid
• You can list at least two factor pairs for a composite number
• You can explain why a number is composite
• You can play a game to find composite numbers

Why this matters

Knowing about composite numbers helps you understand how numbers work and how they can be broken down into smaller parts. In the multiplication grid, composite numbers are like busy bees – they show up in many places because they can be made in different ways. This is useful in many areas like sharing things equally, solving puzzles, and understanding how things fit together.

For example, if you have 12 cookies and want to share them with friends, you can make groups of 2, 3, 4, or 6. That’s because 12 is a composite number – it has more than one way to be made by multiplying.

How it works

Let’s start by understanding what a composite number is:

1. First, think of a number like 6.
2. Now, find all the ways you can multiply two numbers to get 6.
3. These are the factor pairs: 1 × 6 and 2 × 3.
4. Since 6 has more than one way to be made by multiplying, it is a composite number.

Now let’s look at how the multiplication grid shows us this:

• Each cell in the grid shows the result of multiplying two numbers.
• When a number appears more than once in the grid, it’s likely a composite number.
• For example, 12 appears at 3 × 4, 2 × 6, and 1 × 12.

Examples you can see

Let’s look at some numbers in the multiplication grid to see which ones are composite:

Notice how these numbers all have more than one way to be made. Let’s explore how this works in a real-life situation:

Ages 4-6: Imagine you have 12 toy cars and want to split them into equal groups. You can make 1 group of 12, 2 groups of 6, 3 groups of 4, or 4 groups of 3. That’s why 12 is a composite number!

Ages 7-9: Think of a garden that is 12 square metres. It can be shaped as 1 row of 12, 2 rows of 6, 3 rows of 4, or 4 rows of 3. These are all ways to make 12 square metres, showing that 12 is composite.

Ages 10-12: If you are planning a party and have 18 invitations, you can make 1 row of 18, 2 rows of 9, 3 rows of 6, or 6 rows of 3. That’s a lot of ways to arrange your invitations – showing that 18 is composite.

Try it as a mini adventure

Adventure: The Factor Hunt!

You are on a mission to find all the composite numbers in the multiplication grid from 1 to 12. Your goal is to find at least 5 composite numbers and list their factor pairs.

Start with the grid and look for numbers that appear more than once. For example:

1. First time: Find 6. Factor pairs are 1 × 6 and 2 × 3.
2. Second time: Find 8. Factor pairs are 1 × 8 and 2 × 4.
3. Third time: Find 9. Factor pairs are 1 × 9 and 3 × 3.
4. Fourth time: Find 10. Factor pairs are 1 × 10 and 2 × 5.
5. Fifth time: Find 12. Factor pairs are 1 × 12, 2 × 6, and 3 × 4.

Now, draw a picture of how you can arrange 12 items into groups to show its factor pairs. You can use blocks, counters, or draw circles to represent the groups.

Common mistakes

• Mistake: Thinking that 1 is a composite number.
• Why it happens: Some children confuse composite with prime numbers.
• Fix: Remember, 1 only has one factor pair: 1 × 1. So it’s neither prime nor composite.
• Mistake: Thinking that prime numbers are composite.
• Why it happens: Children might mix up the definitions of prime and composite.
• Fix: Prime numbers have exactly two factor pairs (1 × number), while composite numbers have more than two.
• Mistake: Only looking for one factor pair for a number.
• Why it happens: Some children stop after finding one way to multiply.
• Fix: Keep looking for all the ways you can make that number by multiplying two smaller numbers.

Parent and carer guide

Helping your child understand composite numbers can be fun and simple:

• Use everyday objects like counters, blocks, or even snacks to show how a number can be split into groups.
• Ask questions like: “How many ways can we split 12 cookies into equal groups?”
• Draw or build arrays to show how numbers can be made in different ways.
• Play the Factor Hunt game together – it’s a great way to practice.
• Don’t worry if your child gets confused at first – it’s normal to mix up the terms. Keep practicing and it will become clearer.

Practice questions

1. Which of these numbers is composite? 7, 8, 9, 11. What are their factor pairs?
2. Find three composite numbers between 1 and 20. List their factor pairs.
3. How many factor pairs does 16 have? List them.
4. Is 15 a composite number? Why or why not?
5. Draw an array to show how 10 can be made by multiplying two numbers.

Answers:

1. 8 and 9 are composite. 8: 1 × 8, 2 × 4. 9: 1 × 9, 3 × 3.
2. Example answers: 4 (1 × 4, 2 × 2), 6 (1 × 6, 2 × 3), 10 (1 × 10, 2 × 5).
3. 16 has 4 factor pairs: 1 × 16, 2 × 8, 4 × 4.
4. Yes, 15 is composite. Its factor pairs are 1 × 15 and 3 × 5.
5. Draw 2 rows of 5 or 5 rows of 2 to show 10 = 2 × 5 or 10 = 5 × 2.

FAQ

What is a composite number?

A composite number is a number that has more than two different factor pairs. That means it can be made by multiplying two numbers in more than one way.

How is a composite number different from a prime number?

A prime number has exactly two factor pairs: 1 × itself. A composite number has more than two factor pairs.

Why do we need to know about composite numbers?

Understanding composite numbers helps with division, fractions, and problem-solving. It also helps you see how numbers can be broken down into smaller parts.

Can you give an example of a number that is not composite?

Yes, 1 is not composite because it only has one factor pair: 1 × 1. Also, prime numbers like 2, 3, 5, 7, 11 are not composite.

How can I help my child practice?

You can use everyday objects like counters or snacks to make groups. Play games like the Factor Hunt or draw arrays to show how numbers can be made in different ways.