There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Factors. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Factors Starters:

Abundant Buses: A game based around the concept of factors and abundant numbers.

Dancing: Work out how many people were at the dance from the clues given.

Factuples: Spot the factors and the multiples amongst the numbers in the grid.

Flabbergasted: If each number in a sequence must be a factor or multiple of the previous number what is the longest sequence that can be made from the given numbers?

Four Factors: Find four single digit numbers that multiply together to give 120. How many different ways are there of answering this question?

Hotel Digital: A puzzle about the lifts in a hotel which serve floors based on the day of the week.

Perfect Numbers: Six is a perfect number as it is the sum of its factors. Can you find any other perfect numbers?

Vixen Value: The Vixen Value of a word is the number of vowels multiplied by the number of consonants. How many words can you find with Vixen Value of 24?

Back To The Factory: Find all the numbers below 1000 which have exactly 20 factors

Calendar Riddle: Work out the date of my birthday from the clues in rhyme.

Divisible by 11: Can you prove that a three digit number whose first and third digits add up to the value of the second digit must be divisible by eleven?

HCF and LCM given: If given the HCF, LCM can you find the numbers?

Nine Digit Numbers: How many different nine digit numbers are their that contain each of the digits from one to nine?

Reverse Connection: Find a general rule for the difference between a two digit number and that same number with the digits reversed.

Victorian Times Comparison: Is 10! larger or smaller than the number of seconds in six weeks?

Weather Reports: Which five different integers multiply together to give 12?

Zero Even: Prove that zero is an even number.

#### Number Grids

Investigate the properties of number with these interactive number grids.

Transum.org/go/?to=grids

### Curriculum for Factors:

#### Year 5

Pupils should be taught to identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers more...

Pupils should be taught to know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers more...

Pupils should be taught to establish whether a number up to 100 is prime and recall prime numbers up to 19 more...

Pupils should be taught to solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes more...

#### Year 6

Pupils should be taught to use common factors to simplify fractions; use common multiples to express fractions in the same denomination more...

Pupils should be taught to identify common factors, common multiples and prime numbers more...

#### Years 7 to 9

Pupils should be taught to use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property more...

### Exam-Style Questions:

There are almost a thousand exam-style questions unique to the Transum website.

### Feedback:

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

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"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

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"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
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"This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles."

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"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
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"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

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### Notes:

A factor is a whole number that divides exactly into another whole number. We say the first number is a factor of the second number. Prime numbers only have two factors, one and themselves.

After becoming familiar with times tables pupils then practise using this knowledge by recognising factors of numbers. There are well known and some less well known divisibility tests that are of some use in solving more complex number problems.

Pupils need to know how to find the highest common factor (HCF) of two or more numbers either mentally or using a pen and paper strategy so that they can correctly manipulate fractions and algebraic expressions.

### Factors Teacher Resources:

Number Grids: Investigate the properties of number with these interactive number grids.

HCF and LCM Calculator: A demonstration of how to find the highest common factor (HCF or GCD) and the lowest common multiple (LCM) of two numbers.

Divisibility Tests 2-12: A visual aid designed to be projected in the classroom. Here you can find the quick ways of telling whether a number is exactly divisible by the numbers two to twelve.

Prison Cell Problem: A number patterns investigation involving prisoners and prison guards.

Sieve of Eratosthenes: A self checking, interactive version of the Sieve of Eratosthenes method of finding prime numbers.

### Factors Activities:

Number Grids: Investigate the properties of number with these interactive number grids.

Prime Numbers Jigsaw: Interactive jigsaw puzzles of different types of grids containing prime numbers.

Factor Trees: Create factor trees to find the prime factors of the given numbers.

Factor Pairs: Find the factor pairs of the given numbers and arrange them in order.

Flabbergasted Game: This game for one or two players is an exciting challenge to demonstrate an understanding of factors and multiples.

How Many Factors?: Work out the number of factors a number has then write them all as a list.

Prime Labyrinth: Find the path to the centre of the labyrinth by moving along the prime numbers.

Connect 4 Factors: This a game for one or two players. The winner is the first to line up four numbers with a common factor.

Pick The Primes: Pick the prime fruit from the tree as quickly as possible. Practise to improve your personal best time.

HCF and LCM: Practise finding the highest common factor (H.C.F), sometimes called the greatest common divisor, and the lowest common multiple (L.C.M) of two numbers.

Factor Trees Challenge: Can you determine the unique digits that will complete these factor trees?

Times Square: Practise your times tables with this self-checking multiplication grid.

Divisibility Test: Practise using the quick ways to spot whether a number is divisible by the digits two to nine.

Algebraic HCF: Exercises providing practice finding the highest common factor of algebraic expressions.

Algebraic LCM: Exercises providing practice finding the lowest common multiple of algebraic expressions.

Factorising: Practise the skills of algebraic factorisation in this structured online self marking exercise.

Scallywags and Scoundrels: Arrange the scallywags and scoundrels on the chairs so that the numbers of any two sitting next to each other add up to a prime number.

Prison Cell Problem: A number patterns investigation involving prisoners and prison guards.

Product Square: Arrange the given numbers in a three by three grid to obtain the diagonal, row and column products.

Satisfy: Place the nine numbers in the table so they obey the row and column headings about the properties of the numbers.

Threes and Fives: A game for two players who take turns to add a domino to the line in order to score threes and fives.

Three Ways: Find three different ways of multiplying four different digits together to get the given target number. There are nine levels for this online challenge.

Doughnut Dissection: A puzzle to find four different ways of making 900 by multiplying together three different numbers.

Delightfully Divisible: Arrange the digits one to nine to make a number which is divisible in the way described.

Sieve of Eratosthenes: A self checking, interactive version of the Sieve of Eratosthenes method of finding prime numbers.

Square and Cube Roots: Find square roots and cube roots by first calculating the prime factorisation of a number.

### Factors Investigations:

Aunt Sophie's Post Office: Investigate the ways of making up various postage amounts using 3p and 8p stamps. An online stamp calculator is provided for you to check your working.

### Factors Videos:

Transum's Factors Video

Prime Numbers Video: A reminder of what prime numbers and composite numbers are.

Finding Prime Factors: A straight forward explanation from SLEP

HCF and LCM Video: Learn different methods for finding the highest common factor and lowest common multiple of two or three numbers.

### Factors Worksheets/Printables:

Divisibility Tests Worksheet: This worksheet contains a list of the divisibility tests along with a fill-in-the-table exercise.

Links to other websites containing resources for Factors are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

### Search

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### Other

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#### Square and Cube Roots

Find square roots and cube roots by first calculating the prime factorisation of a number.

Transum.org/go/?to=scroots

### Teaching Notes:

Many Transum activities have notes for teachers suggesting teaching methods and highlighting common misconceptions. There are also solutions to puzzles, exercises and activities available on the web pages when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

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