Let \(\mathbb{Z}[\sqrt{5}i]\) be the set of all complex numbers of the form \(z=a+b\sqrt{5}i\), where \(a\) and \(b\) are integers. How many prime factors does the number 6 have in \(\mathbb{Z}[\sqrt{5}i]\)?

Did I mention that this is a trick question (or a tricky question, anyway)? Before answering, you may want to read up on "primes" and "irreducibles," taking note of the fact that the two concepts are not equivalent.

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