Play this game and see if you can figure out the computer's chosen number.

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...

A collection of resources to support work on Factors and Multiples at Secondary level.

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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!?

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

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

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

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

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?

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

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Is there an efficient way to work out how many factors a large number has?

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?

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

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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.

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.

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

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

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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

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?

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

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?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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

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 I. . . .

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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?

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?

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?

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

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

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

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

This article for teachers describes how number arrays can be a useful representation for many number concepts.

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

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

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.

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