Only 62 out of 1,136 reviewed make the cut.

Lots of families can't afford to pay the full sticker price that a college charges.

So, universities, especially private schools, are increasingly awarding institutional and federal dollars to help families chip away at their sometimes sky-high price tags.

Among them, a few dozen colleges and universities meet 100 percent of demonstrated financial need. That means that they use a combination of loans, scholarships, grants and work-study to fill the gap between the cost of attendance – room and board, tuition, fees and other expenses – and what a family can contribute.

[Discover how to determine whether a college is affordable for you.]

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The amount a family can pay is typically determined by the information they provide on the Free Application for Federal Student Aid, including tax data, assets and family size. Some schools' formulas may also include information not provided on the FAFSA.

Of the 1,136 colleges and universities that submitted financial need data to U.S. News, just 62 of them report covering full need for undergraduate students in fall 2014.

[Explore 10 tools that give you a tailored estimate of what you'll pay for college.]

Most of the schools with this financial aid policy are highly ranked private colleges and universities. Among them are Princeton University, ranked No. 1 among National Universities, and Williams College, ranked first among National Liberal Arts Colleges.

Overall, nearly two-thirds of schools meeting full need for undergraduates rank within the top 20 of their categories. About one-third place in the top 10 of their categories.

[Discover the 2016 Best Value Schools.]

One group of schools nearly absent from this list is public universities. While they tend to have lower sticker prices than their private peers, just a couple of public schools meet full need, including the University of Virginia and University of North Carolina—Chapel Hill.

Below are the colleges and universities that claimed to meet 100 percent of demonstrated financial need for full-time, degree-seeking undergraduates in fall 2014.

The financial need data above are correct as of Sept. 14, 2015. For complete financial aid data, full rankings and much more, access the U.S. News College Compass.

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CORRECTION: A headline on this story previously said only .05 percent of colleges meet full financial need, when it should've said 5 percent. We messed up the math.

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