You may also like

problem icon

What an Odd Fact(or)

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

problem icon

Counting Factors

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

problem icon

Repeaters

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.

Remainder

Age 11 to 14 Challenge Level:

What is the remainder of $2^{2002}\div 7?$

decorative image.

What happens with different powers of $2$?

Try to explain the mathematics behind what you discover.