factors problem solving year 5

Factors and Multiples KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Age 7 to 11 Challenge Level

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Abundant Numbers

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Flashing Lights

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

The Moons of Vuvv

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Mystery Matrix

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

One Wasn't Square

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Multiplication Squares

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Factor Lines

Age 7 to 14 challenge level.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Two Primes Make One Square

Can you make square numbers by adding two prime numbers together?

Cycling Squares

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Which Is Quicker?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Up and Down Staircases

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Factors and Multiples Game

Age 7 to 16 challenge level.

This game can replace standard practice exercises on finding factors and multiples.

Factor-multiple Chains

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Picture a Pyramid ...

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Counting Cogs

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Factor Track

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Square Subtraction

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Dicey Array

Age 5 to 11 challenge level.

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

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Factors Lesson

This Year 5 Factors lesson covers the prior learning of factor pairs, before moving onto the main skill of factors.

The lesson starts with a prior learning worksheet to check pupils’ understanding. The interactive lesson slides recap the prior learning before moving on to the main skill. Children can then practise further by completing the activities and can extend their learning by completing an engaging extension task.

National Curriculum Objectives Mathematics Year 5: (5C5a) Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers

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Lesson Slides

These lesson slides guides pupils through the prior learning of factor pairs, before moving onto the main skill of factors. There are a number of questions to check pupils' understanding throughout.

Modelling PowerPoint

This powerpoint can be used to model the questions that the children will complete on the Varied Fluency and Reasoning & Problem Solving worksheets as part of this lesson.

These are the same as the lesson slides on Classroom Secrets. You can assign this as an activity for pupils to access individually in school or remotely from home.

Video Tutorial

Jade shows pupils how to find the factors of different numbers using arrays in this Factors Video Tutorial.

1 Prior Learning

This worksheet recaps prior learning of factor pairs, before moving onto the main skill of factors.

Interactive Activity

This Year 4 Factor Pairs IWB Activity includes three questions designed to check pupils' understanding of factor pairs.

2 Practical Activities

Supporting Activity

This factors supporting activities sheet contains suggestions for additional tasks you might wish to use to support pupils' understanding of the concepts taught in the lesson.

2 Varied Fluency

This differentiated worksheet includes varied fluency questions for pupils to practise the main skill of this lesson.

This Year 5 Multiples and Factors Game includes five questions designed to check pupils' understanding of multiples and factors.

2 Reasoning & Problem Solving

This differentiated worksheet includes reasoning and problem solving questions to support the teaching of this step.

Mixed Practice

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of factors.

Discussion Problem

This worksheet includes two discussion problems which can be used in pairs or small groups to further pupils' understanding of the concepts taught in this lesson.

Interactive Challenge Activity

This Year 5 Factors Maths Challenge tests pupils' understanding of identifying factors and finding common factors.

This differentiated worksheet includes varied fluency and reasoning and problem solving questions to support the teaching of this step.

2 Additional Activities

Home Learning Pack

This Autumn week 8 Maths pack contains varied fluency, reasoning and problem solving worksheets.

Consolidation Pack

This resource is aimed at Year 5 Expected and has been designed to give children the opportunity to consolidate the skills they have learned in Autumn Block 4 – Number: Multiplication and Division.

Learning Video Clip

The organisers of the Qatar Olympic Games need help with determining the best way to organise where people park, sit and stand at the swimming and diving events at the games. They need to use their understanding of factors to help them.

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Factors and Multiples Worksheets

Welcome to our Factors and Multiples Worksheets. Here you will find a wide range of free Math Worksheets which will help your child to learn to use multiples and factors at a 4th Grade/ 5th Grade level.

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Factors and Multiples Worksheet

These sheets have been designed to support your child with their learning of multiples and factors.

The sheets are graded in order of difficulty with the easiest sheet coming first in each section.

Using these sheets will help your child to:

Want to test yourself to see how well you have understood this skill?.

Try our NEW quick quiz at the bottom of this page.

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Multiples and Factors Help

Multiples worksheets, factors worksheets.

Factors and Multiples Online Quiz

If a number is a multiple of another number, it means that it can be made out of adding groups of the other number together.

12 is a multiple of 4 because 4 + 4 + 4 = 12 (or 4 x 3 = 12)

27 is a multiple of 9 because 9 + 9 + 9 = 27 (or 9 x 3 = 27)

17 is not a multiple of 4 because it cannot be made by adding groups of 4 together.

A factor is a number that divides into another number with no remainder.

In other words every number is divisible by each of its factors.

1 is a factor of every whole number, because every integer is divisible by one.

3 and 7 are both factors of 21 because 3 x 7 = 21

10 and 6 are both factors of 60 because 10 x 6 = 60

7 is not a factor of 24 because 24 is not divisible by 7 (24 ÷ 7 = 3 remainder 3).

Multiples and Factors are connected with each other:

The example below shows the relationship visually.

If we know that 3 is a factor of 24, then 24 must be a multiple of 3.

If we know that 24 is a multiple of 3, then 3 must be a factor of 24.

Multiples and Factors Worksheets

We have split our worksheets into 3 different sections:

We have two worksheets on finding Factor Pairs up to 100.

We have two worksheets which involve finding all the factors of different numbers.

Factor and Multiples Riddles

Using riddles is a great way to get children to apply their knowledge of factors and multiples to solve problems.

It is also a good way to get children working collaboratively and talking about the language together.

Each riddle consists of some clues and a selection of possible answers.

Solving the clues gradually eliminates all the incorrect answers leaving just one solution.

Looking for some easier Multiples Sheets

The sheets in this section cover similar areas to the worksheets on this page but are at an easier level.

Looking for some harder Factors and Multiples Worksheets

We also have some more advanced worksheets about multiples and factors.

The worksheets below are more suitable for 6th graders and above.

More Recommended Math Resources

Take a look at some more of our worksheets similar to these.

Divisibility Rules 1-10 Chart

We have a range of charts which can help you determine whether a number between 1 and 10 is a factor of a number.

Divisibility Rules 1-10 Charts

Balancing Math Equations Worksheets

The sheets in this area will help your child understand the use and purpose of the equals sign (=) in an equation.

It will also help children learn to start manipulating and calculating numerical expressions so that they are equivalent.

This will stand them in good stead for when they start to learn algebra, and manipulate algebraic equations.

Balancing Math Equations

Sieve of Erastosthenes

The Sieve of Erastosthenes is a method for finding what is a prime numbers between 2 and any given number.

Eratosthenes was a Greek mathematician (as well as being a poet, an astronomer and musician) who lived from about 276BC to 194BC.

If you want to find out more about his sieve for finding primes, and print out some Sieve of Eratosthenes worksheets, use the link below.

Sieve of Eratosthenes page

Want to find out more about primes?

Take a look at our Prime Number page which clearly describes what a prime numbers is and what they are not.

There are also many different questions about prime numbers answered, as well as information about the density of primes.

What is a Prime Number

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This quick quiz tests your knowledge and skill with factors and multiples here!

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COMMENTS

Year 5 Factors Reasoning and Problem Solving
Questions 1, 4 and 7 (Problem Solving). Developing Find missing factors within a multiplication square where the end number for.
Year 5 Common Factors Reasoning and Problem Solving
Questions 1, 4 and 7 (Problem Solving). Developing Identify the pair of numbers that share the most common factors by systematically checking each times
Year 5 Diving into Mastery: Step 3 Factors Teaching Pack
This superb mastery-style teaching pack has a presentation to use with the whole class, together with a resource of fluency, reasoning and problem-solving
Year-5-Maths-Factors.pdf
Questions 3, 6 and 9 (Reasoning and Problem Solving). Developing Spot the odd one out when using arrays to multiply factors. Requires knowledge of the 2, 3
Factors and Multiples KS2
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it? Dicey Array. Age 5 to 11
Year 5 Multiples Reasoning and Problem Solving
Reasoning and Problem Solving. Step 1: Multiples. National Curriculum Objectives: Mathematics Year 5: (5C5a) Identify multiples and factors
Year 5 Prime Numbers Reasoning and Problem Solving
Greater Depth Use 4 digit cards to make composite numbers up to 50 with prime factors that meet specified criteria. Questions 2, 5 and 8 (Problem Solving).
Factors Year 5 Multiplication and Division Resource Pack
Step 2: Factors Year 5 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Autumn
Year 5 Factors Lesson
This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of factors. Login to download. Classroom
Factors and Multiples Worksheet
apply knowledge of multiples and factors to solve problems;; Develop and practice their mental calculation skills. Want to test yourself to see how well you