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These are the Transum resources related to the statement: "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".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- 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.
- Convoluted Find the runs of four multiples in order as quickly as you can.
- Delightfully Divisible Arrange the digits one to nine to make a number which is divisible in the way described.
- Divisibility Test Practise using the quick ways to spot whether a number is divisible by the digits two to nine.
- 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.
- Divisibility Tests Worksheet This worksheet contains a list of the divisibility tests along with a fill-in-the-table exercise.
- Doughnut Dissection A puzzle to find four different ways of making 900 by multiplying together three different numbers.
- Dump-A-Dice Race An online board game for two players involving prime and square numbers and making choices.
- Factor Trees Create factor trees to find the prime factors of the given numbers.
- Finding Prime Factors A straight forward explanation from SLEP
- Flabbergasted Game This game for one or two players is an exciting challenge to demonstrate an understanding of factors and multiples.
- Goal Products Arrange the numbered footballs on the goal posts to make three, 3-number products that are all the same.
- 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.
- 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.
- Number Grids Investigate the properties of number with these interactive number grids.
- Number Skills Inventory A checklist of basic numeracy techniques that every pupil should know.
- Pick The Primes Pick the prime fruit from the tree as quickly as possible. Practise to improve your personal best time.
- Prime Labyrinth Find the path to the centre of the labyrinth by moving along the prime numbers.
- Prime Numbers Video A reminder of what prime numbers and composite numbers are.
- Prime Pairs Game A game for two players who take turns to select two numbers that add up to a prime number.
- Prime Pips in Pots This is a version of Wari, one of the oldest known games to still be widely played today. It involves small prime numbers.
- Prime Square Drag the numbers into the red cells so that the sum of the three numbers in each row and each column is a prime number.
- 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.
- 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.
- 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.
- Three Prime Sum A self-marking challenge to write each of the given numbers as the sum of three prime numbers.
- 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.
- Venn Diagram Place each of the numbers 1 to 16 on the correct regions on the Venn diagram.
- What Are They? An online exercise about sums, products, differences, ratios, square and prime numbers.

Here are some exam-style questions on this statement:

- "
*Find the highest common factor (HCF) of 60 and 96.*" ... more - "
*Without using a calculator:*" ... more - "
*Write 250 as a product of powers of its prime factors.*" ... more - "
*Show that 206 can be written as the sum of a power of five and a square number.*" ... more - "
*The number, \(N\), can be written as the product of prime factors in index form as:*" ... more

Here is an Advanced Starter on this statement:

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Factors 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.
- LCM LCM stands for lowest common multiple or least common multiple. The LCM of two (or more numbers) is the smallest number that both of the numbers divide into exactly. Being able to find the LCM is useful when trying to find a common denominator when adding two fractions together. The LCM also describes the points when two (or more) periodic repetitions coincide. HCF stands for highest common factor which is also known as the greatest common factor. The HCF of two (or more) numbers is the largest number that divides into the two numbers exactly. Being able to find the HCF is useful in everyday organisational tasks and also when factorising algebraic expressions.
- Number Spotting patterns is an important skill in many areas of life. The world of numbers contains many fascinating patterns and understanding them enables better problem solving strategies. From seeing patterns in the multiples of numbers shaded in a hundred square to spotting the recurring sequences of digits in decimal numbers there is a great deal for pupils to be introduced to. This topic includes even, odd, prime, triangular, perfect, abundant, square and cube numbers. It uses factors and multiples to find solutions to real life problems and encourages number connections to be investigated for pleasure. There are a lot of puzzles, challenges and games too. See also the Mental Methods topic and our Number Skills Inventory.

Do you need a reminder about prime and composite numbers? Watch this video:

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.