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

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

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. . . .

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

In how many ways can the number 1 000 000 be expressed as the product of three 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.

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

How many noughts are at the end of these giant numbers?

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

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

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?

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?

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?

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.

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.

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .

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

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.

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

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

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

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

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

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

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?

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?

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

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

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.

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

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

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.

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

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

Is there an efficient way to work out how many factors a large number has?

Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.

Prove that if the integer n is divisible by 4 then it can be written as the difference of two squares.

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

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

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

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!?

An environment which simulates working with Cuisenaire rods.

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

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

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

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?

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.