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

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?

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?

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

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

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

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!?

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

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.

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. . . .

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.

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

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.

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?

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?

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. . . .

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

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

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

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?

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

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.

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

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

A game that tests your understanding of remainders.

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?

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

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

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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.

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.

Number problems at primary level that may require resilience.

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

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

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?

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?

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

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?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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?

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?

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

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?

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?

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.

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