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kvale
You have the right of it. More precisely, take the logarithim. Then the problem becomes finding a sum of log prime factors that is closest to log(N)/2. This problem is reducible to the subset sum problem, which is NP-hard.
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Although exact solutions are exponential, heuristics can sometimes generate good answers with minimal effort. One example of a heuristic that might work well is the greedy heuristic. To fill a box of size log(N)/2, put the largest factor into the box. Then put the next largest factor that still fits in the box and insert it. Keep doing this until no more factors fit.
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The above will get you the largest factor <= sqrt(N). To get the smallest factor >= sqrt(N), put all the factors in a box, and take them out again largest to smallest, until no more can be taken out. Finally, comapre the two answers to find the closest.
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Update: fixed a typo.
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-Mark
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