Federal grants are very much EFC driven. The main fed grant is the Pwll which for 2008-2009 required an EFC of below 4042 (the EFC cut off changes every year but actually went down for 2008-2009 although the maximum Pell went up). Other federal grants such as ACG and SMART are dependent on Pell eligibility as well as other criteria. SEOG depends on each school but many schools require a 0 EFC for SEOG.
