The greatest common factor of 45m and 6m^5 is 3m. Here's how to find a greatest common factor:
1). Figure out the greatest number that divides evenly into every number in a given set. In your case, the number is 3.
2). Figure out the greatest number of variables that each of the monomials share. In your case, both of your monomials have at least 1 m. This can simply be represented as m.
The final answer is the answers you get from steps 1 and 2 combined.
I hope this helps you out! I have a feeling that my wording might be confusing. If you have any questions, ask me as a comment.