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stacks of coins of various heights
Some colleges will come up with more money than others.
Jeffrey Coolidge—Getty Images

If you're hoping to get enough grants and scholarships to pay for college without any loans, sorry to say the odds are against you.

About three-quarters of undergraduates get less scholarship or grant money than they need to afford college without taking on debt. In fact, the average college reports providing enough aid to meet only 66% of the financial needs of students.

And the gaps in in financial aid tend to be the biggest for those who need it most: Undergraduates from working- and middle-class families—those from families earning between $30,000 and $65,000 a year—receive, on average, about $9,400 less in grants than the federal government calculates the student needs to afford college without loans, according to federal education statistics. To be clear: That's $9,400 on top of the family's "Expected Family Contribution" (EFC) —the amount the government thinks a family can afford. The average financial aid gap for students from families earning more than $105,000, for example, is about $3,500.

(Students from families earning less than $48,000 a year can use Money’s free Affordable College Finder to identify colleges likely to admit them and provide enough aid so that they can graduate without burdensome student loans.)

Officially, colleges tell students and families that they award need-based financial aid on a few standard factors that families report on the Free Application for Federal Student Aid, or FAFSA: the family's size and income, the number of children in college, and any unusually large non-retirement savings or investments

But the official rules and numbers hide some surprising variations and potential opportunities. After all, some students get full rides. Nearly half of all undergraduates get enough aid (or attend such low-cost schools) that they can graduate with little to no debt, while almost 20% of students get financial aid awards that leave a "gap" of more than $14,000 beyond their federal EFC.

College aid officials and independent financial aid analysts say that in reality, the amount of need-based financial aid you'll get typically also depends on five other factors:

(1) What your college can afford. Some schools and some states fund higher education more generously than others. Some states, for example, have cut their higher ed funding so much that their public colleges typically meet less than a third of what the federal government estimates their students need to afford college.

In all, fewer than 150 of the nation's more than 1,500 public and private four-year colleges say it is their policy to provide enough grants to meet at least 90% of the “demonstrated financial need” of undergraduates. And most of those are private, highly selective schools.

But there's a lot of variation even within those supposedly "generous" colleges: Some of the most generous schools, such as Princeton and Yale, will, in many cases, award need-based grants even to students from families earning more than $200,000 a year. Others tend to limit their need-based aid to students from families earning less than about $150,000.

You can see what percentage of need a school typically meets, and the percentage of its students who receive need-based and merit-based aid, on sites like Money.com/colleges, Collegedata.com, and CollegeBoard.org.

Related: The 28 Best Colleges for Need-Based Financial Aid

(2) How much the college "needs" you. Many colleges divvy up their scarce financial aid dollars not by how much the students need, but by how much the college "needs" the student, says Lynn O'Shaughnessy, author of The College Solution. Students with better grades and test scores, or other qualifications that make them attractive candidates, get more generous aid packages at schools that use "preferential packaging," such as Muhlenberg College. "The more attractive the student is academically, the more likely the aid package will be better. So being near the top of the heap among applicants will boost the chances of capturing a great award," O'Shaughnessy notes.

As a general rule, if the school doesn't typically meet 100% of all students' need, you'll probably get an above-average aid package if your academics put you in the top 25%, and a below-average one if you're in the bottom 25%. You can check those scores on Money.com, the federal College Navigator, or Collegedata.com.

(3) Your expected financial contribution. Just about every college expects students to pay something toward their college costs beyond the expected parental contribution. Some notably generous colleges, such as Princeton, only expect students to contribute a few thousand dollars a year, which they can usually earn through work-study and summer jobs. Others, such as Boston College, expect students to contribute through both earnings and loans. “At Boston College the typical freshman has a total self-help expectation of $8,300, composed of a $3,500 federal loan, savings from summer work, and work during the school year,” explains Nanci Tessier, BC’s vice provost for enrollment management. You can call the colleges on your list to ask what their standard student contribution is.

(4) How the school defines "family." All federal and state financial aid, as well as the scholarships awarded by about 80% of colleges, base their need-based awards on the federal definition of a student's family—which is the parent (or parents) with whom the student lives the majority of the time. That means that students of divorced parents who live with a moderate-earning mother, say, could qualify for need-based aid at most colleges no matter how much their father earns.

Related: FAFSA FAQs: Answers to the 10 Most Common College Aid Questions

But more than 150 colleges—mostly elite private schools—take into account the income of the non-custodial parent too. These schools typically require aid applicants to fill out an additional aid application, the College Board's CSS/PROFILE, which, unlike the FAFSA, asks about the income of divorced parents.

Schools that use the CSS/PROFILE typically reduce a student's need-based aid award because of a non-custodial parent's income even if the parents' divorce decree relieved, say, a father of college funding responsibilities, explains John B. Leach, director of financial aid at Emory University. Leach says the hidden income of divorced parents is one reason Emory and many other schools report charging surprisingly high net prices to students who report low incomes on the federal aid forms.

Nearly 40 of the colleges that claim to have generous need-based financial aid charge an average of more than $15,000 a year to students who report family incomes of less than $30,000 to the federal government. Emory reports charging those students a little less than $12,000 a year. On the other end of the spectrum, 12 of the elite schools typically charge low-income students less than $4,000 a year—an amount that usually be covered by work-study jobs or small, federal low-interest loans. (If your school isn't on the list of those requiring the CSS/PROFILE, then the non-custodial parent's income probably won't affect your aid award.)

(5) What the school counts as wealth. The 80% of colleges that determine their aid using only the FAFSA, generally reduce need-based aid only if a family has unusually large savings or investments outside of retirement accounts, or valuable real estate in addition to their home (such as a vacation home). The colleges that use the CSS/PROFILE, however, can, and often do, reduce need-based aid because of the value of a small business, parents' equity in their home, the overall value of their investments, and even, in some cases, the value of their vehicles.