what number has the prime factorization 2 to the third power x 3 to the second power x 5 to the second power?

Answer 1

Well, work it out...

2^3 * 3^2 * 5^2
8 * 9 * 25
1800

Answer 2

Probably not. I'll support my claim by considering the fact that there is no definite way of showing a number is prime. If the 'primeness' of a number cannot be determined, how do you suggest we determine the factors of any number in relation to another? ADDITION: I'm aware of primalty tests such as using the Wilson's Theorem (quite frankly, this is one of the two that I know that guarantees 100%) mentioned by Icarus, however, they are inefficient and it's more useful to consider probabilistic (not sure if this is the word) tests. Using the test for 100 is already extremely difficult. Further addition: The twin prime conjecture is a good example of why we don't know anything about this. ADDITION on Further addition: n is prime and n + 2 is prime. We cannot tell whether infinitely many cases of this exists. If we know what happens from n to n + 1 and n + 1 to n + 2, we would know what happens from n to n + 2. ADDITION: Alright cheeser... I admit defeat. ADDITION: Cheeser, there is nothing wrong in the logic. If j and k are coprime, m and n are also coprime. You missed out "relatively prime" in his answer.