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

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.

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

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

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

A game that tests your understanding of remainders.

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.

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

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

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?

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?

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?

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

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

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. . . .

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?

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

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?

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

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

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

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

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

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

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. . . .

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

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

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

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

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?

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" .

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

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?

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

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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

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

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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?"

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

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

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!?

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

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?

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .

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. . . .