A game that tests your understanding of remainders.

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

Given the products of diagonally opposite cells - can you complete this Sudoku?

A game in which players take it in turns to choose a number. Can you block your opponent?

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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!?

Can you find a way to identify times tables after they have been shifted up?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

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

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?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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

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.

Can you find any perfect numbers? Read this article to find out more...

Follow this recipe for sieving numbers and see what interesting patterns emerge.

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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

Can you complete this jigsaw of the multiplication square?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths. . . .

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?