No factorial is applied on a non integer intermediate result indeed, but if the intermediate result "becomes integer again", factorial are tried.
For example, if a candidate is (1/2) * 3 * 4 + 5, then the algorithm won't try to compute any factorial of (1/2) * 3 = 1.5, but it will consider (1/2) * 3 * 4 = 6.0 as integer and try the factorial on 6.
Note however that I did not pretend to have an exhaustive search, just a "brute" one to find a solution. I changed "enumerating all the candidate" to "enumerating the candidate" to remove some confusion.