### Counting Factors

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

### 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.

### Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

# Remainder

##### Age 11 to 14 Challenge Level:

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

What happens with different powers of $2$?

Try to explain the mathematics behind what you discover.