# Prime factorization question

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• September 16th 2009, 08:36 AM
ordinalhigh
Prime factorization question
We have $E=(\mathbb{E}, +,*,0)$ where $\mathbb{E}$ is the set of even natural numbers. I know all numbers in this set can be factored into a product of $\mathbb{E}$-primes and that it is not always unique.

I'm trying to find the least even number with three factorizations and the least even number that has four factorizations.
• September 16th 2009, 12:12 PM
Bruno J.
$360=2(2\times 3^2)(2 \times 5) = (2 \times 3)^2(2 \times 5) = 2(2\times 3 \times 5)(2 \times 3)$

Pretty sure that's the one for three factorisations!