TITLE: Prime factor of a composite three digit integer
QUESTION [7 upvotes]: Q: What is the largest possible prime factor of a composite three digit integer?
A: The largest $3$-digit is $999$ and $\sqrt {999}=31.61....$ and the largest prime factor less than this is $31$.
The above is one example showing in the discrete math textbook under theorem 
If $n$ is composite, then $n$ has a prime divisor $p$ such that $p\le \sqrt n$.
I found this question is unfounded. Let's say $37$. Basically it is one of the prime factor of $740$. So the answer provided is wrong. Am I right? I think the answer should be $499$.

REPLY [2 votes]: If the question is:  

What is the largest possible minimum prime factor of a composite three digit integer?

(or something similar) then the answer as given by the book, $31$, is correct, because any composite number must have a factor less than or equal to its square root. 
Otherwise, as already observed, a number of the form $2p$ with $p$ prime will give you the largest prime factor of a composite, in this case $499$.