# 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.
$360=2(2\times 3^2)(2 \times 5) = (2 \times 3)^2(2 \times 5) = 2(2\times 3 \times 5)(2 \times 3)$