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?

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

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?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

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!?

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?

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?

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

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

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

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

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.

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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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. . . .

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

A game that tests your understanding of remainders.

Can you work out some different ways to balance this equation?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Have a go at balancing this equation. Can you find different ways of doing it?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Number problems at primary level that may require determination.

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

Number problems at primary level that require careful consideration.

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

Here is a chance to play a version of the classic Countdown Game.

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.

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

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

Can you complete this jigsaw of the multiplication square?

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?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?