Resources tagged with: Factors and multiples

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Broad Topics > Numbers and the Number System > Factors and multiples

There's Always One Isn't There

Age 14 to 16 Challenge Level:

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

Missing Multipliers

Age 7 to 14 Challenge Level:

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

A First Product Sudoku

Age 11 to 14 Challenge Level:

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

Inclusion Exclusion

Age 11 to 14 Challenge Level:

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

Factoring a Million

Age 14 to 16 Challenge Level:

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

Data Chunks

Age 14 to 16 Challenge Level:

Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

Different by One

Age 14 to 16 Challenge Level:

Can you make lines of Cuisenaire rods that differ by 1?

Diagonal Product Sudoku

Age 11 to 16 Challenge Level:

Given the products of diagonally opposite cells - can you complete this Sudoku?

How Old Are the Children?

Age 11 to 14 Challenge 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?"

Counting Cogs

Age 7 to 14 Challenge Level:

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

Product Sudoku

Age 11 to 16 Challenge Level:

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

Take Three from Five

Age 14 to 16 Challenge Level:

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Cuisenaire Environment

Age 5 to 16 Challenge Level:

An environment which simulates working with Cuisenaire rods.

Factorial

Age 14 to 16 Challenge Level:

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

Star Product Sudoku

Age 11 to 16 Challenge 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.

Stars

Age 11 to 14 Challenge Level:

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Substitution Transposed

Age 11 to 16 Challenge Level:

Substitution and Transposition all in one! How fiendish can these codes get?

Times Right

Age 11 to 16 Challenge 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?

Shopping Basket

Age 11 to 16 Challenge Level:

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

Got it for Two

Age 7 to 14 Challenge Level:

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

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.

Have You Got It?

Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target?

Gabriel's Problem

Age 11 to 14 Challenge Level:

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

Common Divisor

Age 14 to 16 Challenge Level:

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

Sieve of Eratosthenes

Age 11 to 14 Challenge Level:

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

Eminit

Age 11 to 14 Challenge 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?

Got It

Age 7 to 14 Challenge 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.

Can You Find a Perfect Number?

Age 7 to 14

Can you find any perfect numbers? Read this article to find out more...

Thirty Six Exactly

Age 11 to 14 Challenge Level:

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

Even So

Age 11 to 14 Challenge 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?

What a Joke

Age 14 to 16 Challenge Level:

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

Remainders

Age 7 to 14 Challenge 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?

Factoring Factorials

Age 11 to 14 Challenge Level:

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

What Numbers Can We Make?

Age 11 to 14 Challenge Level:

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

Satisfying Statements

Age 11 to 14 Challenge Level:

Can you find any two-digit numbers that satisfy all of these statements?

Factors and Multiples Game for Two

Age 7 to 14 Challenge Level:

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

Robotic Rotations

Age 11 to 16 Challenge Level:

How did the the rotation robot make these patterns?

What Numbers Can We Make Now?

Age 11 to 14 Challenge Level:

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

Transposition Cipher

Age 11 to 16 Challenge Level:

Can you work out what size grid you need to read our secret message?

Factor Track

Age 7 to 14 Challenge Level:

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.

Charlie's Delightful Machine

Age 11 to 16 Challenge Level:

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

Cuboids

Age 11 to 14 Challenge 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?

Mathematical Swimmer

Age 11 to 14 Challenge Level:

Can you work out how many lengths I swim each day?

Shifting Times Tables

Age 11 to 14 Challenge Level:

Can you find a way to identify times tables after they have been shifted up or down?

The Remainders Game

Age 7 to 14 Challenge Level:

Play this game and see if you can figure out the computer's chosen number.

LCM Sudoku II

Age 11 to 18 Challenge Level:

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

Hot Pursuit

Age 11 to 14 Challenge 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...

Ben's Game

Age 11 to 16 Challenge Level:

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

American Billions

Age 11 to 14 Challenge 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...

Neighbourly Addition

Age 7 to 14 Challenge Level:

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?