Factoring technique, faster than trial division?

[paul at fatmans.demon.co.uk]

just an idea I came up with today, I don`t suggest it is a fast 
factoring method, but it would be interesting to know if it is faster 
than say trial division:

Calcuate a composite number H such that H has a large number of prime 
factors (hundreds).

now  use the euclidean algorithm to try to find a gcd of X (the 
number being factored) and H, if there is none try a new H, if there 
is you have found a factor.

It is hardly elegant but I would nevertheless be interested to see if 
it is apreciably faster than other kludge methods like trial 
division. 


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