Mini Minds Hub · Free printable
Factor Detectives Match-Up: Free Printable Game for Year 4
- ForYear 4
- StageKey Stage 2
- CostFree
- FormatPrintable PDF
Factor Detectives Match Up is a free printable maths game for Year 4 (ages 8 to 9). Children act as detectives and match each number to all of its factors. They use what they know from the times tables to spot factor pairs and check that no clue has been missed. It needs only a pencil, and page 2 gives the grown-up notes, help for children who find it hard and a stretch idea.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to your child and keep page 2 for yourself. Black and white printing works well on plain A4 paper.
What is on the sheet
Children play detective with numbers. Each number on the sheet has a set of factors that belong to it, and the job is to match every number to all of its factors. To do this, children think about which pairs of numbers multiply to make each number. They use their times tables as clues, and they need to find all the factors, not just the first few that come to mind.
Worked example: all the factors of 40
Find all the factors of 40.
This example uses a different number from the sheet. It shows two ways to hunt for factors.
Method 1: work through the pairs in order- Start with 1. 1 x 40 = 40, so 1 and 40 are factors.
- Try 2. 2 x 20 = 40, so 2 and 20 are factors.
- Try 3. No whole number times 3 makes 40, so 3 is not a factor.
- Try 4. 4 x 10 = 40, so 4 and 10 are factors. Try 5. 5 x 8 = 40, so 5 and 8 are factors.
- Try 6 and 7. Neither works. The next number to try would be 8, which we already have, so we can stop.
- Take 40 counters or buttons.
- Share them into equal rows with none left over. 1 row of 40, 2 rows of 20, 4 rows of 10 and 5 rows of 8 all work.
- The number of rows and the length of each row are both factors. Write them all down in order.
How to hunt for factors
Start with 1
Every whole number has 1 as a factor, and every whole number is also a factor of itself. Write these two down first. They make the first pair.
Try the numbers in order
Test 2, then 3, then 4, and so on. Ask: does this number times something make my number? Use the times tables as your clue book.
Write the partner each time
When you find a factor, find its partner straight away. Writing both saves time and helps you see the pairs.
Know when to stop
When the next number you would test is one you have already found as a partner, you have met in the middle. There are no more factors to find.
What is a factor?
A factor of a number is a whole number that divides into it exactly, with nothing left over. Factors come in pairs, because two whole numbers multiply together to make the number. This is why times tables are so useful. Every multiplication fact you know is also a pair of factors, so the facts children learn for speed turn out to be clues for finding factors too.
In Year 4, the National Curriculum asks children to recognise and use factor pairs in multiplication and division work. Finding all the factors of a number is a good test of organised thinking. Children need a method, such as working through the numbers in order, so that they do not miss any. It also shows that multiplication and division are linked.
Skills and curriculum link
- Finding factor pairs
- Times tables recall
- Multiplication and division links
- Working in order
- Logical thinking
- Checking your work
Ways to help a young detective
- Pairs firstAsk your child to say which two numbers multiply to make the number. Once they find one pair, they have found two factors.
- Use the tablesIf your child knows a times table well, ask whether the number appears in it. This is a quick way to find a clue.
- Be systematicEncourage them to test 1, 2, 3 and so on in order. A clear order stops factors being missed.
- Explain the choiceAsk: how do you know that one belongs? Saying the multiplication out loud shows whether the idea is secure.
Key words
- FactorA whole number that divides exactly into another number, with nothing left over.
- Factor pairTwo whole numbers that multiply together to make a number.
- MultiplyFind the total of equal groups. 3 groups of 4 is 3 x 4.
- ProductThe answer to a multiplication.
- MultipleA number in a times table. 10, 15 and 20 are multiples of 5.
- DivideShare or group a number into equal parts.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2 for the grown-up.
- Work through one number at a time. Ask: which pairs multiply to make it?
- Do the first go together. Talk about each choice and why it fits.
- Check against the notes on page 2. Ask your child how they decided, not only what they chose.
- Come back to it another day. Repeating a familiar activity builds confidence.
Help, stretch and game ideas
If it feels too hard
Draw out the pairs for 12 first: 1 x 12, 2 x 6, 3 x 4. Then read off the factors from the pairs. Write each pair in a neat list so your child can see them. Use counters in rows if it helps.
To stretch confident children
Find all the factors of 24 and 30 on your own. Then compare your two lists. Which number has more factors? Explain how you know that you have found every factor and that none is missing.
Make it a game
Pick a number up to 30. Your partner has 60 seconds to list every factor. One point for each correct factor. Swap roles after each round. Play a set number of rounds and see who has the highest score.
Mistakes to watch for
Watch forA child lists multiples instead of factors. For 5, they write 5, 10, 15.
Try thisRemind them that factors divide into the number and are never bigger than it. Ask: which numbers multiply to make 5?
Watch forA child forgets 1 and the number itself.
Try thisSay that every number has these two factors. Always start the list with the pair 1 and the number.
Watch forA child finds one factor in a pair but not its partner.
Try thisEach time they find a factor, ask: what do I multiply it by to get the number? Write both partners down together.
Talk about it
- How do you know that these two numbers belong together?
- Which times table helped you most? Why?
- Can you think of a number that has only a few factors?
- How will you know when you have found all the factors?
- Why do factors come in pairs?
- Is it quicker to start with small numbers or big ones? Explain.
Take it off the page
Counter rows
Take a handful of counters, buttons or pasta shapes. Find every way to arrange them in equal rows with none left over. Write the multiplications you find.
Factor hide and seek
Write a number on a piece of paper. A partner writes factors on small cards and hides one. Find the missing factor by working out which multiplication is incomplete.
Tables hunt
Write out a few times tables on paper. Pick a number and tick every table it appears in. Then say what those ticks tell you about its factors.
Who it is for
Parents
Sit beside your child for the first go, then let them lead. Ask them to explain each match out loud. If they get stuck, try drawing the pairs for a smaller number first. Praise careful, organised thinking.
Teachers
Use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing. Page 2 has support and stretch ideas for mixed ability groups, and the skills list helps you match it to your planning.
Home educators
Use it on its own or as part of a wider maths plan. It pairs well with times tables practice and everyday talk. You can print it again for brothers and sisters or for revision a few weeks later.
Where this fits in
Before this, children learn the times tables and see that multiplication and division are linked. They also work with equal groups and arrays, which show why numbers can be shared into equal rows. Knowing these facts well makes factor hunting much easier.
After this, children use factors in many ways. Later in Key Stage 2, they meet common factors, prime numbers and square numbers. They also use factors to help with mental multiplication and with simplifying fractions.
Questions parents and teachers ask
- What age is Factor Detectives Match Up for?
It is written for Year 4 (ages 8 to 9), in Key Stage 2. It also works as revision for older children who need to feel more confident with factors and times tables.
- What will children practise?
Children recognise factor pairs and find all the factors of a number using the multiplication tables. This supports the Year 4 multiplication and division strand of the National Curriculum for England.
- What if it feels too hard?
Start with a smaller number and draw out the pairs. For 12, write 1 x 12, 2 x 6 and 3 x 4, then read off the factors. Counters in equal rows also help.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters, other pupils or revision, so the same sheet can be used more than once.
- Is it suitable for teachers to use in class?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 includes support and stretch ideas.
- Is this a screen free activity?
Yes. It is a printable that needs only paper and a pencil. That makes it a good choice for quiet time, rainy days, school holidays or a calm moment away from devices.
- Do I need to print in colour?
No. It prints well in black and white on plain A4 paper. Print both pages, give page 1 to your child and keep page 2 for the grown-up.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.