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.

i. How many four digit square numbers are composed of even numerals?

ii. What four digit square numbers can be reversed and become the square of another number? Can you explain why?