Seeing as you didn't say an "empty/air-filled" barrel it can be anything, as long as it was lighter than any contents it pushed out of the barrel. (or since you didn't say, only put something in it, lighter than anything he removed from it).
Easy enough. All you'd have to do is try all the prime numbers that are less than the Square Root of the number you listed and you'll come up with all the factors. Being as the square root of that number is between 385 and 386, I really don't feel like sitting here all day figuring that out so someone else can do the math.
Oh the technique and what to do is easy enough. It wasn't much of a challenge to state what needed to be done. Frankly though, it's not worth the effort to do it.
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