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

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?

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

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

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

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

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?

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

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.

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!?

Number problems at primary level that may require resilience.

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

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

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.

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

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. . . .

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

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

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Resources to support understanding of multiplication and division through playing with number.

More resources to support understanding multiplication and division through playing with numbers

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.

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?

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?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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. . . .

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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?

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

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

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?

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

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?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

This Sudoku requires you to do some working backwards before working forwards.

Related resources supporting pupils' understanding of multiplication and division through playing with numbers.

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

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?

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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.

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?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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