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'.

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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!?

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?

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?

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

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

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

Factors and Multiples game for an adult and child. How can you make sure you win this game?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

These two group activities use mathematical reasoning - one is numerical, one geometric.

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Can you make square numbers by adding two prime numbers together?

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

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either. . . .

This activity creates an opportunity to explore all kinds of number-related patterns.

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?