X Tables
Times Table Methods

Factor pairs for primary learners

Find all factor pairs for a number and use them to understand products.

Quick answer

Factor pairs are two numbers that multiply together to make a specific number. For example, the factor pairs of 12 are 1×12, 2×6, and 3×4.

Learning outcome

By the end of this page, you will be able to find all the factor pairs for any number up to 100. Success signs:
  • You can list all the factor pairs for a given number
  • You understand that factor pairs are two numbers that multiply to make that number
  • You can find factor pairs by using arrays or repeated addition
  • You can explain how factor pairs help you understand multiplication and division

Why this matters

Factor pairs help you understand how numbers work together in multiplication and division. When you know the factor pairs of a number, you can:
  • Quickly solve multiplication problems
  • Find all the ways to split a number into equal groups
  • Understand how numbers are built from smaller parts
  • Help with division problems
In real life, factor pairs are useful when you're sharing items equally, planning a party, or working with arrays in games or art projects.

How it works

To find factor pairs, you need to think about what two numbers multiply to make your target number. You start with 1 and work your way up, checking if each number divides evenly into your target number. Step-by-step:
  1. Start with 1 and the number you're working with
  2. Check if 2 divides evenly into your number
  3. If yes, write down the pair
  4. Continue with 3, 4, 5, and so on
  5. Stop when you reach a number that is bigger than the square root of your number

Examples you can see

Let's find the factor pairs for 12. Step 1: Start with 1 and 12 1 × 12 = 12 Step 2: Check 2 2 divides into 12 evenly (12 ÷ 2 = 6) So 2 × 6 = 12 Step 3: Check 3 3 divides into 12 evenly (12 ÷ 3 = 4) So 3 × 4 = 12 Step 4: Check 4 We already have 4 × 3 = 12, so we stop here. The factor pairs for 12 are:
  1. 1 × 12
  2. 2 × 6
  3. 3 × 4
Here's a visual way to see this:
Factor Factor Product
1 12 12
2 6 12
3 4 12

Try it as a mini adventure

The Treasure Hunt Challenge You are a treasure hunter looking for a hidden chest. The chest is locked with a code that requires you to find all the factor pairs for the number 24. You must find all the ways to split 24 items into equal groups to unlock the chest.
  1. First time: Find the factor pair 1 × 24
  2. Second time: Check if 2 works (24 ÷ 2 = 12)
  3. Third time: Check if 3 works (24 ÷ 3 = 8)
  4. Fourth time: Check if 4 works (24 ÷ 4 = 6)
  5. Fifth time: Check if 5 works (24 ÷ 5 = 4.8 - not a whole number)
  6. Sixth time: Check if 6 works (24 ÷ 6 = 4) - you already have 4 × 6
The treasure chest opens with these factor pairs:
  • 1 × 24
  • 2 × 12
  • 3 × 8
  • 4 × 6

Common mistakes

  • Mistake: Forgetting to check if a number divides evenly into your target number.
    Why it happens: Children might not understand division or might skip steps.
    Fix: Use a calculator or count by that number to check if it fits evenly.
  • Mistake: Thinking that 12 = 2 × 6 is the only way to split 12 items.
    Why it happens: Not knowing that factor pairs come in pairs.
    Fix: Always check if you can make equal groups with other numbers.
  • Mistake: Stopping too early and missing factor pairs.
    Why it happens: Not knowing that you only need to check up to the square root.
    Fix: Remember to keep checking until you reach a number that's bigger than the square root.

Parent and carer guide

How to help your child:
  • Start with small numbers like 6, 8, or 12 to practice
  • Use objects like counters or blocks to show factor pairs
  • Ask questions like "What two numbers multiply to make 12?"
  • Play games where you race to find factor pairs
  • Use real-life examples like sharing 12 cookies equally among friends
What to watch for:
  • Does your child understand that factor pairs are two numbers that multiply to make the target number?
  • Are they checking numbers systematically?
  • Do they understand that factor pairs come in pairs?
What not to worry about:
  • It's okay if they don't get all factor pairs at first
  • They may make mistakes - that's part of learning
  • Some children learn better with hands-on materials

Practice questions

  1. What are the factor pairs for 10?
  2. Find all factor pairs for 15.
  3. What are the factor pairs for 18?
  4. Write down the factor pairs for 20.
  5. Find all factor pairs for 25.
Answers:
  1. 1 × 10, 2 × 5
  2. 1 × 15, 3 × 5
  3. 1 × 18, 2 × 9, 3 × 6
  4. 1 × 20, 2 × 10, 4 × 5
  5. 1 × 25, 5 × 5

FAQ

What are factor pairs?

Factor pairs are two numbers that multiply together to make a specific number. For example, 3 and 4 are a factor pair for 12 because 3 × 4 = 12.

How do I find all factor pairs for a number?

Start with 1 and the number itself, then check each number up to the square root of your target number. If a number divides evenly into your target number, you've found a factor pair.

Can a number have factor pairs that are the same?

Yes! When a number is a perfect square, it can have a factor pair where both numbers are the same. For example, 4 × 4 = 16, so 4 and 4 are a factor pair for 16.

Why do factor pairs matter?

Factor pairs help you understand how numbers are built from smaller parts. They're useful for multiplication, division, and understanding the relationships between numbers.

Are factor pairs the same as factors?

Not exactly. Factors are all the numbers that divide evenly into a number. Factor pairs are two numbers that multiply together to make that number. Every factor pair contains two factors.