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

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?

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!?

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

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

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.

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

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

56 406 is the product of two consecutive numbers. What are these two numbers?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

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?

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" .

Number problems at primary level that may require resilience.

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

What is the remainder when 2^{164}is divided by 7?

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Can you find different ways of creating paths using these paving slabs?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?

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

This task combines spatial awareness with addition and multiplication.

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

What is the least square number which commences with six two's?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?