# Resources tagged with: Factors and multiples

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Broad Topics > Properties of Numbers > Factors and multiples ### How Old Are the Children?

##### Age 11 to 14Challenge Level

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?" ### Diagonal Product Sudoku

##### Age 11 to 16Challenge Level

Given the products of diagonally opposite cells - can you complete this Sudoku? ### Gabriel's Problem

##### Age 11 to 14Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was? ### Star Product Sudoku

##### Age 11 to 16Challenge Level

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid. ### Got it for Two

##### Age 7 to 14Challenge Level

Got It game for an adult and child. How can you play so that you know you will always win? ### American Billions

##### Age 11 to 14Challenge Level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3... ### Ben's Game

##### Age 11 to 16Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with? ### LCM Sudoku

##### Age 14 to 16Challenge Level

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it. ### A First Product Sudoku

##### Age 7 to 14Challenge Level

Given the products of adjacent cells, can you complete this Sudoku? ### Repeaters

##### Age 11 to 14Challenge Level

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13. ### Statement Snap

##### Age 7 to 14Challenge Level

You'll need to know your number properties to win a game of Statement Snap... ### The Remainders Game

##### Age 7 to 14Challenge Level

Play this game and see if you can figure out the computer's chosen number. ### Have You Got It?

##### Age 11 to 14Challenge Level

Can you explain the strategy for winning this game with any target? ##### Age 11 to 16Challenge Level

The items in the shopping basket add and multiply to give the same amount. What could their prices be? ### Multiples Sudoku

##### Age 11 to 14Challenge Level

Each clue in this Sudoku is the product of the two numbers in adjacent cells. ### Product Sudoku

##### Age 11 to 16Challenge Level

The clues for this Sudoku are the product of the numbers in adjacent squares. ### Big Powers

##### Age 11 to 16Challenge Level

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas. ### Different by One

##### Age 14 to 16Challenge Level

Can you make lines of Cuisenaire rods that differ by 1? ### Factors and Multiples - Secondary Resources

##### Age 11 to 16Challenge Level

A collection of resources to support work on Factors and Multiples at Secondary level. ### Four Coloured Lights

##### Age 11 to 14Challenge Level

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up? ### Counting Factors

##### Age 11 to 14Challenge Level

Is there an efficient way to work out how many factors a large number has? ##### Age 11 to 14Challenge Level

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . . ### Stars

##### Age 11 to 14Challenge Level

Can you work out what step size to take to ensure you visit all the dots on the circle? ### Got It

##### Age 7 to 14Challenge Level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target. ### Factorial

##### Age 14 to 16Challenge Level

How many zeros are there at the end of the number which is the product of first hundred positive integers? ### Cuboids

##### Age 11 to 14Challenge Level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all? ### Times Right

##### Age 11 to 16Challenge Level

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find? ### Just Repeat

##### Age 11 to 14Challenge Level

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence? ### Remainders

##### Age 7 to 14Challenge Level

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be? ### Factor Lines

##### Age 7 to 14Challenge Level

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

##### Age 11 to 14Challenge Level

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why? ##### Age 11 to 14Challenge Level

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born? ### X Marks the Spot

##### Age 11 to 14Challenge Level

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" . ### Eminit

##### Age 11 to 14Challenge Level

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M? ### Can You Find a Perfect Number?

##### Age 7 to 14 ### Factors and Multiples Game for Two

##### Age 7 to 14Challenge Level

Factors and Multiples game for an adult and child. How can you make sure you win this game? ### Factoring Factorials

##### Age 11 to 14Challenge Level

Find the highest power of 11 that will divide into 1000! exactly. ### Number Families

##### Age 11 to 14Challenge Level

How many different number families can you find? ### Oh! Hidden Inside?

##### Age 11 to 14Challenge Level

Find the number which has 8 divisors, such that the product of the divisors is 331776. ### What Numbers Can We Make Now?

##### Age 11 to 14Challenge Level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now? ### Expenses

##### Age 14 to 16Challenge Level

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time? ### Thirty Six Exactly

##### Age 11 to 14Challenge Level

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors? ### Sieve of Eratosthenes

##### Age 11 to 14Challenge Level

Follow this recipe for sieving numbers and see what interesting patterns emerge. ### Missing Multipliers

##### Age 7 to 14Challenge Level

What is the smallest number of answers you need to reveal in order to work out the missing headers? ### Hot Pursuit

##### Age 11 to 14Challenge Level

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same... ### What Numbers Can We Make?

##### Age 11 to 14Challenge Level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make? ### Funny Factorisation

##### Age 11 to 16Challenge Level

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors? ##### Age 11 to 14Challenge Level

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it? ### Charlie's Delightful Machine

##### Age 11 to 16Challenge Level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light? ### Even So

##### Age 11 to 14Challenge Level

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?