Guessing a number with 250 divisors

Alice and Bob play the following number guessing game.

• First Alice picks an integer $n$ with exactly $250$ positive divisors. These divisors include $1$ and $n$, and are denoted as $1=d_1<d_2<d_3<\cdots<d_{249}<d_{250}=n$.
• Then Bob may query these divisors by paying a fee of $x$ Euro per query to Alice. Such a query simply consists of an index $i$ with $1\le i\le250$.
• If Bob already knows the value of the divisor $d_{251-i}$ (since he has asked it in an earlier query, or since he is able to deduce it from the knowledge gained so far), then Alice answers the query with the word "BOOM".
• If Bob does not know the value of $d_{251-i}$, then Alice answers the query with the value of $d_i$.
• The game ends, as soon as Bob knows $n$ and announces it to Alice. Bob then receives $600$ Euros from Alice.

Question: What is the largest fee $x$, for which Bob can still avoid (with absolute certainty) to lose any money?