Prime numbers

problem
Thirty six exactly

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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?
problem
A biggy

Age

14 to 16

Challenge level

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
problem
Em'power'ed

Age

16 to 18

Challenge level

Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?
problem
Some cubes

Age

16 to 18

Challenge level

The sum of the cubes of two numbers is 7163. What are these numbers?
problem
What's left?

Age

5 to 7

Challenge level

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
problem
Round and round the circle

Age

7 to 11

Challenge level

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.
problem
Prompt cards

Age

7 to 11

Challenge level

These two group activities use mathematical reasoning - one is numerical, one geometric.
article
An introduction to proof by contradiction

An introduction to proof by contradiction, a powerful method of mathematical proof.
game
Favourite

Factors and multiples game

Age

7 to 16

Challenge level

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