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.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Each number will appear as a factor in 100!. So, for example
100! = 100x99x98x...where 22is a factor of 100, 2 is a
factor of 98 and 25 is a factor of 96. Are there
patterns to the powers of the number that appear as you consider
each term of the factorial? Can this pattern be generalised for