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Counting Factors

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


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.


Age 11 to 14 Challenge Level:

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

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What happens with different powers of $2$?

Try to explain the mathematics behind what you discover.