In search of a better algorithm for finding factors

Problem 12 has me stuck. The obvious algorithm for finding factors of numbers is too slow to find the first triangle number (1, 1+2, 1+2+3, etc.) to have 500 factors. There should be a solution that takes less than a minute, but Brute Force is not the answer, since they are not distributed in any sort of pattern that I can see. I can't think about it any more today, but I'll be chewing it over in my subconscious (in theory). Or maybe I'll just be thinking about how to go 7-under-par in Wii Golf.