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Common Factors and Multiples: Free Printable Worksheet for Year 6

  • ForYear 6
  • StageKey Stage 2
  • CostFree
  • FormatPrintable PDF
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Common Factors and Multiples is a free printable maths worksheet for Year 6 (ages 10 to 11), in Key Stage 2. Children list common factors, find the highest common factor (HCF) and find the lowest common multiple (LCM). It needs only a pencil, and 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 begin by listing the common factors of two numbers. They then find the HCF of several pairs, including one where both numbers are in the twenties or thirties. After that they write out the first few multiples of two numbers and use them to find the LCM, before finding more LCMs on their own. There is space under each numbered question for working and an answer.

  • List the common factors of 12 and 18.
  • Find the HCF of 8 and 12.
  • Find the HCF of 15 and 25.
  • Find the HCF of 24 and 36.
  • Write the first three multiples of 4 and of 6. Find the LCM.
  • Find the LCM of 3 and 5.
  • Find the LCM of 6 and 8.
  • Find the LCM of 4 and 10.

Worked example: HCF and LCM of 14 and 21

Find the HCF and the LCM of 14 and 21.

This example uses different numbers from the sheet. It shows how to work with two lists.

Method 1: HCF by listing factors
  1. List the factor pairs of 14: 1 and 14, 2 and 7. So the factors are 1, 2, 7, 14.
  2. List the factors of 21: 1 and 21, 3 and 7. So the factors are 1, 3, 7, 21.
  3. The common factors are 1 and 7. The biggest of these is 7.
Method 2: LCM by listing multiples
  1. Write the multiples of 14: 14, 28, 42.
  2. Write the multiples of 21: 21, 42.
  3. The first number to appear in both lists is 42.
HCF = 7 and LCM = 42

Factors, multiples and why they matter

A factor is a whole number that divides exactly into another number, with nothing left over. A multiple is a number you reach by multiplying a number by 1, 2, 3 and so on, so multiples are the numbers in its times table. Factors are found by splitting a number up. Multiples are found by counting on. Keeping those two ideas apart is the heart of this sheet.

Common factors and common multiples turn up again and again in later maths. Common factors help when simplifying fractions. Common multiples help when adding fractions with different denominators. Children who can list factors and multiples in an organised way find both jobs much easier. Good times table knowledge makes the lists quicker to write and easier to check.

Skills and curriculum link

  • Finding factors
  • Listing multiples
  • Common factors
  • HCF
  • LCM
  • Working in an organised way

This sheet supports the area below. It is matched to the published England framework. Please check it against your own school plan.

Framework Subject or area Strand Year
National Curriculum (England) Maths Addition, subtraction, multiplication and division Year 6

What children will be able to do

  • I can list the factors of two numbers.
  • I can find the highest common factor.
  • I can find the lowest common multiple.

Ideas that help

  • Factors come in pairsEvery factor has a partner that it multiplies with to make the number. Writing the pairs in order helps children avoid missing any.
  • Every number has 1 as a factorOne divides exactly into every whole number, so 1 is always a common factor of any two numbers. The question is whether there is a bigger one.
  • A number is a factor and a multiple of itselfAny number is its own biggest factor and its own smallest multiple above zero. This is a handy check when a list looks odd.
  • Use the times tablesKnowing the tables lets children spot factors quickly and write multiples without counting on one at a time.

Key words

  • FactorA whole number that divides exactly into another number. 7 is a factor of 14.
  • Factor pairTwo numbers that multiply to make a given number. 7 and 2 are a factor pair of 14.
  • MultipleA number in a times table. 7, 14 and 21 are multiples of 7.
  • Common factorA number that is a factor of both numbers you are looking at.
  • HCFThe highest common factor. It is the biggest number that is a factor of both numbers.
  • LCMThe lowest common multiple. It is the smallest number above zero that is a multiple of both numbers.

How to use it

  1. Print both pages. Page 1 is for your child. Keep page 2, which has the notes and answers.
  2. Ask your child to say in their own words what a factor is and what a multiple is before they begin.
  3. For the first question, ask them to list every factor in pairs for each number, then look for the matches.
  4. Let them try the HCF and LCM questions, then check together using page 2. Ask, "How do you know you have found them all?"
  5. Come back another day and redo any questions that felt tricky. Repeating a familiar sheet builds confidence.

Help, stretch and game ideas

If it feels too hard

Write the factors or multiples of each number in two lists, one under the other. Circle the numbers that appear in both. For factors, work in pairs, starting at 1. For multiples, keep going until a circled match appears. Try the first questions together.

To stretch confident children

Find the HCF and the LCM of 18 and 30. Then find two numbers that have an HCF of 1 and look at their LCM. Ask what you notice. Try a few more pairs to test your idea.

Make it a game

Write the numbers 2 to 30 on slips of paper and put them in a bag. Each player draws two slips. Both race to find the HCF and the LCM. One point for each correct answer. First to ten points wins.

Mistakes to watch for

Watch forA child mixes up HCF and LCM and gives a number that is too big or too small.

Try thisSay it out loud: factors are found by splitting a number, so the HCF cannot be bigger than either number. Multiples are found by counting on, so the LCM cannot be smaller than either number.

Watch forA child stops listing factors too early and misses a pair, so the HCF is wrong.

Try thisWrite the factors in pairs, starting at 1 and working upwards. Stop only when the pairs meet in the middle.

Watch forA child lists multiples but picks a common multiple that is not the smallest one.

Try thisWrite the multiples in order for both numbers and circle the first match. Read the lists from the left and stop at the first circle.

Talk about it

  • What is the difference between a factor and a multiple?
  • How can you be sure you have found every factor of a number?
  • Why is 1 always a common factor of two numbers?
  • Can the HCF of two numbers ever be bigger than the smaller number? Why not?
  • Can the LCM of two numbers ever be smaller than the bigger number? Why not?
  • Where might you need a common multiple in real life?

Take it off the page

Counter rectangles

Take a handful of counters. Arrange them in as many different rectangles as you can. Each rectangle shows a factor pair of your number.

Chalk number track

Draw a track of numbers on the pavement. One child hops on multiples of 2 and another on multiples of 7. Call out the numbers where both land.

Clap and stamp

Count aloud together. Clap on the multiples of one number and stamp on the multiples of another. Listen for when you clap and stamp at once.

Who it is for

Parents

Sit beside your child for the first question, then let them lead. Ask them to explain how they know they have every factor. If they get stuck, suggest two lists side by side. Praise careful working as well as right answers.

Teachers

Use it as a starter, plenary, early finisher task, homework or supply cover. It needs no preparation beyond printing. Page 2 has support and stretch ideas for mixed ability groups. It pairs well with work on simplifying fractions and common denominators.

Home educators

Print it as part of a wider maths plan and use it again for brothers, sisters or revision later. Ask children to explain their method aloud. Pair it with times table practice and everyday number talk.

Where this fits

Before this sheet, children learn their times tables and see how numbers can be split into factor pairs. They also meet multiples through counting in steps and learn what prime numbers are. Those ideas make the lists on this sheet quicker to write.

After this sheet, children use common factors to simplify fractions and common multiples to find common denominators. Both skills rely on the same organised listing practised here, so confidence with HCF and LCM helps with fractions work.

Check it worked

Ask these when the sheet is finished. Listen for the reasoning, not just the answer.

  1. How do you know you have found all the factors of a number?
  2. What is the difference between a factor and a multiple?
  3. Where might you use a common multiple in real life?

Questions parents and teachers ask

What age is Common Factors and Multiples for?

It is written for Year 6 (ages 10 to 11), in Key Stage 2. It can also be used for revision with older children who need to practise factors and multiples, or as a stretch task for confident younger ones.

What will children practise?

Children list common factors, find the highest common factor and find the lowest common multiple. They also practise writing out multiples and working in an organised way, which helps them check that nothing has been missed.

What is the difference between HCF and LCM?

The HCF is the biggest number that divides exactly into both numbers. The LCM is the smallest number above zero that both numbers divide into. The HCF is never bigger than the smaller number, and the LCM is never smaller than the bigger one.

Are the answers included?

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. Keep it away from your child until they have tried page 1.

Is it free?

Yes. It is free to print for home and classroom use. You can print it again for brothers and sisters, or for revision a few weeks later. Black and white printing on plain A4 paper works well.

Is this a screen free activity?

Yes. It needs only paper and a pencil, so it works well for quiet time, rainy days and school holidays. Writing out factors and multiples by hand also helps children see patterns in the numbers.

Can teachers and home educators use it?

Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. Home educators and tutors can use it alone or as part of a wider plan. It needs no preparation beyond printing.

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Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.

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