To find the greatest number of baseballs that the coach can give to each group, you need to divide the total number of baseballs (300) by the number of groups (9).
Calculating this:
\[ \frac{300}{9} \approx 33.33 \]
Since the coach can only give whole baseballs, the greatest whole number that can be given to each group is 33.
So the answer is 33.