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As per wxffles' comment Simplify[Sqrt[x^3] Sqrt[x - a x]/x, x > 0] Sqrt[1 - a] x


Factoring algorithms work by finding a prime factor, then dividing by it, then continuing on the result, and so the prime factors are found in essentially random order, unless your algorithm is trial division (which I hope to God mathematica does not use). So, the answer to your question is: filtering is your only solution. EDIT On the other hand, the OP's ...

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