This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
Number problems at primary level that may require resilience.
Find the highest power of 11 that will divide into 1000! exactly.
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?
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!?
56 406 is the product of two consecutive numbers. What are these two numbers?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .
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. . . .
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?
Given the products of adjacent cells, can you complete this Sudoku?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
Play this game and see if you can figure out the computer's chosen number.
Can you work out what a ziffle is on the planet Zargon?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
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.
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?
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" .
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.
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?
Can you find different ways of creating paths using these paving slabs?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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.
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
This task combines spatial awareness with addition and multiplication.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
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?
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?
Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?
These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
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.
What is the least square number which commences with six two's?
Number problems at primary level that require careful consideration.
If the answer's 2010, what could the question be?
How would you count the number of fingers in these pictures?