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?

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

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

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

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" .

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

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

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

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?

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?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Number problems at primary level that may require determination.

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

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.

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 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.

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

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

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?

Number problems at primary level that require careful consideration.

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

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?

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. . . .

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

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.

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?

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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?

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

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

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

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

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

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.

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

Can you complete this jigsaw of the multiplication square?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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?

A game that tests your understanding of remainders.

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

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

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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