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

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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!?

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

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?

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

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

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?

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

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Number problems at primary level that may require resilience.

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" .

Can you find different ways of creating paths using these paving slabs?

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?

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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.

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

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?

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?

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?

This task combines spatial awareness with addition and multiplication.

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?

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.

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?

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?

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

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

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?

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?

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!

Resources to support understanding of multiplication and division through playing with number.

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

This challenge combines addition, multiplication, perseverance and even proof.

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

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.

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?

How would you count the number of fingers in these pictures?

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

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

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. . . .