The government says more than half the 7 million undergraduates who enrolled in college full-time last year received financial aid, compared with less than a quarter of the 4.2 million part-time students.

For the 58 percent of the full-time students receiving financial aid, the support from all sources - the federal government, states and the college itself - averaged $3,813, according to a survey released Wednesday by the Department of Education's Center for Statistics.For the rest, the financial aid was $2,199 on average.

Overall, 46 percent of the 11.2 million undergraduates received some type of aid, with 35 percent getting federal help.

While 24 percent of the part-timers got help from some source, less than 1 in 7 got any help from Washington.

The cost of attending college, including tuition, room, board, books and other expenses, averaged $6,000 in the fall of 1986 for the students. They were surveyed last spring about how they were paying for college and what it cost.

The center said 77 percent of all the students attended public colleges, 18 percent private colleges and 5 percent proprietary, or for-profit, trade schools.

The trade school students were far more likely to draw financial aid.

The so-called National Postsecondary Student Aid Survey found that 84 percent of those enrolled in proprietary schools received aid and 81 percent of those got federal help. Nearly 35,000 students were questioned.

That compared with 65 percent of private college students who were getting help, including 48 percent who got aid from Washington; and 38 percent of all public college students, 29 percent of whom got federal aid.

The College Board has reported previously that $20.5 billion in aid was available in 1986-87.