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.

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

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

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

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

A game that tests your understanding of remainders.

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

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

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?

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

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

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

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?

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

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?

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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. . . .

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?

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

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

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?

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?

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?

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

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.

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

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

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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

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?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

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

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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?

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

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?

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

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