From my Army days, that is most likely a laundry mark. The F being the first initial of the soldier’s last name and the last 4 digits of his Army serial number.
a good book to help you with your search is “Finding Your Father’s War” by Jonathan Gawne. http://www.amazon.com/Finding-Your-Fathers-War-Understanding/dp/1932033149
If you have your relative’s name and hopefully birth place as a minimum you can go to the National Archives website: www.archives.gov And from there go to http://www.archives.gov/veterans/ and you can put in a request for his personnel file; please note that nearly 80% of ww2 files were destroyed in a 1973 fire at the National Personnel Records Center in St. Louis, MO; however many records were partially reconstructed.
Which is very sad. I am able to get most of my four great-grandfather's Civil War records but not my Father's WWII records.