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Generally, no. There was a time when Social Security did pay benefits to college students, but the law changed in 1981.
Currently, Social Security pays dependent or survivor benefits only to students attending classes at a secondary school (grade 12 and below). Generally, benefits stop when a student reaches 18, unless the student is disabled or is still attending a secondary school on a full-time basis.

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For a child who is still in school, benefits can continue until he or she graduates or until two months after the 19th birthday, whichever comes first.