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

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?

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

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

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

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

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!?

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

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?

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

Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own. . . .

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. . . .

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

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

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. . . .

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.

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. . . .

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?

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.

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

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

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

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

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

Number problems at primary level that may require resilience.

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.

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

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

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?

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

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

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. . . .

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

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" .

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

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.

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?

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

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

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?

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

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal. . . .

This task combines spatial awareness with addition and multiplication.

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