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?

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.

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?

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 see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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" .

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

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

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

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?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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

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

This problem is designed to help children to learn, and to use, the two and three times tables.

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?

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.

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 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?

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

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.

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Number problems at primary level that may require determination.

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

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. . . .

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.

Number problems at primary level that require careful consideration.

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

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

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

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

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

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

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?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

This number has 903 digits. What is the sum of all 903 digits?

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.

Use the information to work out how many gifts there are in each pile.

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

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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?

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

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

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.

Can you complete this jigsaw of the multiplication square?

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?

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?