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.
Pick three test values - calculate differences (why
are only three listed?) - and then the product. Can you find an
exception? The question is "Why not?".
The second half of the question is about multiples of three. Can
you 'categorise' numbers in terms of their relationship to
mulltiples of three and how does this help?
Have you seen the problem Take
Three from Five ?