The article says:
The fundamental theorem of arithmetic
states that every positive integer can
be factorized in one way as a product
of prime numbers.
This statement has to be appropriately
... we count the factorizations 3x5x13
and 13x3x5 as the same, for instance.
Reading your other comments, it appears you are arguing against something that you actually agree with, and I suspect you have mis-read or mis-interpreted what Gowers has written.