Prime numbers

problem
Favourite

Factors and Multiples Puzzle

Age

11 to 14

Challenge level

2 out of 3

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

Snappy Statements

Age

11 to 14

Challenge level

2 out of 3

Use properties of numbers to work out whether you can satisfy all these statements at the same time.
problem
Favourite

Why 24?

Age

14 to 16

Challenge level

2 out of 3

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
problem
Favourite

Em'power'ed

Age

16 to 18

Challenge level

2 out of 3

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

1 out of 3

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

Prime Counter

Age

16 to 18

Challenge level

1 out of 3

A short challenge concerning prime numbers.
problem

Thirty Six Exactly

Age

11 to 14

Challenge level

2 out of 3

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

Code Breaker

Age

7 to 11

Challenge level

2 out of 3

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?
problem

Just Repeat

Age

11 to 14

Challenge level

3 out of 3

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?
problem

What's Left?

Age

5 to 7

Challenge level

2 out of 3

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