Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

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?"

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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?

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...

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

A game that tests your understanding of remainders.

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

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

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.

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

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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

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

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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

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

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

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?

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

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

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.

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

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

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. . . .

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

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

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

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

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

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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