Multiplication and division

problem
A one in seven chance

Age

11 to 14

Challenge level

What is the remainder when 2^{164}is divided by 7?
problem
A conversation piece

Age

7 to 11

Challenge level

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?
problem
1, 2, 3, 4, 5

Age

7 to 11

Challenge level

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
problem
The number crunching machine

Age

7 to 11

Challenge level

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
problem
Sept03 Sept03 Sept03

Age

7 to 11

Challenge level

This number has 903 digits. What is the sum of all 903 digits?
problem
Which is quicker?

Age

7 to 11

Challenge level

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

Age

11 to 14

Challenge level

Which set of numbers that add to 100 have the largest product?
problem
Remainders

Age

7 to 14

Challenge level

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

Age

7 to 11

Challenge level

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
The clockmaker's birthday cake

Age

7 to 11

Challenge level

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?