iwillsurvive101 wrote:I got stuck finding prime factors of 5304. I have noticed that I repeatedly get stuck finding prime factors of "awkward" numbers, and it seems that its pretty common on advanced questions 650+....is there a short cut that you guys recommend?

You really can't be asked to find prime factors of 'awkward' large numbers on the GMAT, because it just takes far too long. The only large numbers that can be prime factorized in any reasonable amount of time are numbers which are divisible by 2, 3 and/or 5, since we have quick tests that let us see when a number is divisible by those three primes. So you could, perhaps, be asked to prime factorize a number like 3105, because you can quickly tell that you can divide by 5 and also by 9 (summing the digits), and therefore quickly get down to a much smaller number. You could never be asked to prime factorize a number like 12,121, though, since that number has no obvious prime divisors - all you could do is try dividing by 7, by 11, by 13, and so on, hoping to find a prime factor, and that would takes ages to do (don't waste your time doing it, but it is equal to 17*23*31). If you've seen questions which require you to prime factorize 'awkward' numbers, they are certainly prep company questions, and not official ones.

neelgandham wrote:
p.s: Do you know that the largest prime number is 2^(43,112,609)-1

There are infinitely many primes - there can't possibly be a largest prime number. That may be the largest known prime, however.

tpr-becky wrote: finding prime factors of large nubmers is common on GMAT

This isn't true in my experience. I've seen many thousand official GMAT questions, and I'm almost certain the largest actual number I've ever needed to prime factorize was 441 (in a PS question in OG11).

What you do often need to do is prime factorize expressions which represent large numbers - expressions like 3^29 - 3^27 - but in those cases, you are using algebraic factorization techniques, and not long division.