Mini Minds Hub · Free printable
Factors of a Number: Free Printable Worksheet for Year 5
- ForYear 5
- StageKey Stage 2
- CostFree
- FormatPrintable PDF
Factors of a Number is a free printable maths worksheet for Year 5 (ages 9 to 10). Children find the factor pairs of numbers such as 12, 18 and 36, then decide whether one number is a factor of another and count the factors of a number. It takes about 15 minutes and needs only a pencil. Page 2 gives the grown-up notes, help ideas, a stretch task and the answers.
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.
What is on the sheet
Children find the factor pairs of a set of numbers, starting with 12 and moving on through 18, 20, 24, 30 and 36. Each number has space for the pairs to be written down. Near the end they decide whether one number is a factor of another, and they count how many factors a number has. They use their times tables throughout.
- Factor pairs of 12
- Factor pairs of 18
- Factor pairs of 20
- Factor pairs of 24
- Factor pairs of 30
- Factor pairs of 36
- Is 7 a factor of 42? Yes or no
- How many factors does 16 have?
Worked example: factor pairs of 15
Find all the factor pairs of 15.
This number is not on the sheet. It shows two ways children can work.
Method 1: test in order- Write 1 and 15. 1 times 15 makes 15.
- Try 2. 15 is an odd number, so 2 does not go into it exactly. Skip it.
- Try 3. 3 times 5 makes 15. Write 3 and 5.
- Try 4. 4 times 3 is 12 and 4 times 4 is 16, so 4 does not work.
- The next number to try is 5, but it is already in your list. Stop. You have every pair.
- Put 15 counters on the table.
- Make 1 row of 15. That works, so 1 and 15 are a pair.
- Make 3 rows. Each row has 5 counters with none left over, so 3 and 5 are a pair.
- Try 2 rows and 4 rows. Counters are left over each time, so those numbers are not factors.
What is a factor?
A factor of a number is a whole number that divides it exactly, with nothing left over. Factors come in pairs, because two whole numbers multiply together to make the number. Finding factor pairs is really the same job as using times tables, but working backwards. Instead of asking what 4 times 6 makes, children ask which two numbers multiply to make a given number.
In the National Curriculum for England, finding all the factor pairs of a number sits in the number strand, multiplication and division, and children meet it in Year 5. It builds on times tables from earlier years. It also prepares children for simplifying fractions, finding common factors and later work on prime numbers. A calm, ordered method matters more than speed.
Skills and curriculum link
- Finding factor pairs
- Times tables
- Multiplication and division facts
- Working in order
- Spotting patterns in numbers
Helpful ideas for finding factors
- Always start with 11 times any number gives that number. So 1 and the number itself always make a pair. Write that pair first, then look for others.
- Work in orderTry 1, then 2, then 3 and so on. Checking in order stops children missing pairs and helps them keep track.
- Know when to stopWhen the next number you would try is already in your list, you have found every pair. There is no need to go on.
- Use times tables to checkIf a number is a factor, it appears in a times table with the other number in its pair. Say the multiplication out loud to prove it.
Key words
- FactorA whole number that divides another number exactly, with nothing left over.
- Factor pairTwo whole numbers that multiply together to make a number.
- MultipleA number you get by counting in steps of another number, like the numbers in a times table.
- ProductThe answer when you multiply two numbers.
- DivisibleAble to be divided exactly, with no remainder.
- ArrayObjects arranged in equal rows and columns, which shows a multiplication.
How to use it
- Print both pages. Page 1 is for your child. Keep page 2, which has the answers and notes.
- Read the first question together. Ask your child what a factor pair is, in their own words.
- Let them choose how to work: times tables, counters in equal rows, or testing numbers in order. Encourage them to write each pair neatly.
- Check against page 2. Ask, "How do you know you have found them all?" The reasoning matters as much as the answer.
- Come back another day and redo any that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Build each number from counters and share them into equal rows. If the rows come out equal with none left over, you have found a pair. Start with the smaller numbers on the sheet, say each multiplication aloud, and come back to the rest later.
To stretch confident children
Find a number under 50 with exactly 6 factors. Then try to find a second one. Write out the factor pairs for each to prove your answer. Explain to a grown-up how you decided which numbers to try.
Make it a game
Take turns picking a number from 1 to 40. The other player lists all its factors. Score a point for each correct list, and check with a times table or counters if you disagree. First to five points wins.
Mistakes to watch for
Watch forA child writes 1 and the number, then stops, missing the middle pairs.
Try thisAsk them to try 2, then 3, then 4 in order, saying "does it go in exactly?" each time. Counters in equal rows make this easy to see.
Watch forA child lists multiples instead of factors. For 10 they write 10, 20 and 30.
Try thisRemind them that factors are never bigger than the number. Ask which numbers multiply together to make 10.
Watch forA child counts the same number twice, writing 3 and 5 and then 5 and 3 as separate pairs.
Try thisSay that a pair is the same pair in either order. Draw a ring round each number the first time it appears.
Talk about it
- How would you explain what a factor is to a younger child?
- Why do you think 1 is always a factor?
- How do you know when you have found every pair?
- Which times table helped you most today?
- Can you think of a number that has only one pair? What do you notice about it?
- How did you check your answer to the yes or no question?
Take it off the page
Counter rows
Take a handful of counters, buttons or pasta shapes. Share them into equal rows in as many ways as you can. Write down each way as a multiplication.
Factor hunt
Pick a number from a door, a bus ticket or a book page. Find its factor pairs on paper and see who in the family finds them fastest.
Times table wall
Write a times table on a long strip of paper. Circle the pairs of numbers that multiply to make one chosen number, then try a new number.
Who it is for
Parents
Sit beside your child for the first question, then let them lead. About 15 minutes is plenty. If they get stuck, bring out counters or buttons and share them into equal rows together.
Teachers
Use it as a starter after teaching factors, a plenary, an early finisher task or supply cover. It needs only printing. Page 2 has support and stretch ideas for mixed ability groups, plus the answers for quick marking.
Home educators
Pair it with everyday talk about sharing things equally, such as dividing sweets or sorting toys into rows. Use the stretch idea and the game for brothers and sisters, and return to the sheet for revision a few weeks later.
Where this fits in maths
Before this, children learn their times tables and the matching division facts. They also meet multiples, and they learn that multiplication and division are inverse operations. Factors bring these ideas together.
After this, children use factors to find common factors of two numbers, to simplify fractions and to spot prime numbers. Confident factor finding makes all of these topics easier.
Questions parents and teachers ask
- What age is Factors of a Number for?
It is written for Year 5 (ages 9 to 10), in Key Stage 2. Confident Year 4 children can try it, and older children can use it for revision or to build speed with times tables.
- What will children practise?
They practise finding all the factor pairs of a number, using their times tables. They also decide whether one number is a factor of another and count how many factors a number has.
- How long does it take?
It takes about 15 minutes for one child working in pencil. Work through it together the first time, then let your child try alone on another day.
- What if my child finds it hard?
Build each number from counters and share them into equal rows to find the pairs. Say each multiplication aloud. Start with the smaller numbers and come back to the rest another day.
- Does the sheet include answers?
Yes. Page 2 is for the grown-up and has the answers, along with notes on how to use the sheet, help for children who find it hard, and a stretch idea.
- Is it suitable for 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 it works well for mixed ability groups.
- Do I need a screen or colour printer?
No. It is a screen free printable that needs only paper and a pencil. It prints well in black and white on plain A4 paper, so it suits quiet time, rainy days and school holidays.
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.