Lithuanians Nerijus Radavicius, 29 and Justinas Gubinas, 22, were convicted of the rape of the 32-year-old woman which they filmed on a mobile phone.
Ovidijus Kavaliauskas, 22, was found guilty of raping the woman while she was asleep.
The men were each jailed for four years and four months for the assault which took place at a farmhouse on the outskirts Fraserburgh.
Speaking after the verdict Dectective John Swanney of the Police Scotland Protection Unit praised the “strength and courage” of the victim in speaking out against her attackers.
He said: “I would like to pay tribute and thank the female victim involved in this case for speaking out against Gubinas, Kavaliauskas and Radavicius.
“This incident was extremely traumatic for the victim and having to relive it in court will have been very distressing.
DI Swanney continued: “The strength and courage she has shown during the enquiry and subsequent proceedings has enabled the case to be brought before the courts and led to the sentences delivered today.”
The trial of the three men was held at the High Court in Aberdeen and they were sentenced at the High Court in Glasgow today.
Di Swanney said: “I hope that she can move on with her life as best as she can in the knowledge that these men have been brought to justice for the crimes they committed and received significant custodial sentences.”