Find the largest four digit number which has a total of exactly 3 factors. Assuming that 1 and the number itself are factors

Answer 1

you want the largest perfect square less than 10000. The three factors will be 1,√n, and n

Any number not a perfect square will have 4 or more factors (or just 2 factors if it is prime)

Answer 2

The largest prime less than 100 is 97 so the largest four digit number with 3 factors is 97^2=9409.