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'.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Given the products of adjacent cells, can you complete this Sudoku?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Number problems at primary level that may require resilience.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
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?
Play this game and see if you can figure out the computer's chosen number.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
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?
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!?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
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.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
Can you work out what a ziffle is on the planet Zargon?
Can you find different ways of creating paths using these paving slabs?
Choose a symbol to put into the number sentence.
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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 challenge combines addition, multiplication, perseverance and even proof.
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Can you put these four calculations into order of difficulty? How did you decide?
This task combines spatial awareness with addition and multiplication.
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!
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!
A number game requiring a strategy.
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
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?
Number problems at primary level that require careful consideration.
If the answer's 2010, what could the question be?
More resources to support understanding multiplication and division through playing with numbers
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?