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?

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

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

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

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.

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!?

Have you seen this way of doing multiplication ?

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

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

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

A game in which players take it in turns to choose a number. Can you block your opponent?

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. . . .

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

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

A collection of resources to support work on Factors and Multiples at Secondary 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.

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

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

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

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

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

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.

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

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.

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

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

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

A game that tests your understanding of remainders.

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?

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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

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?

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.

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

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Can you find what the last two digits of the number $4^{1999}$ are?

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?

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?"

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

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

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.

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

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?