That's the conclusion they've reached based on confessions of the alleged perpetrators and forensic evidence.
Tomás Zerón de Lucio, the man in charge of criminal investigations, laid out the evidence during a press conference. According to Zerón, who went into great detail, the students were kidnapped, taken to a trash dump, killed, set on fire, the remains put in bags and then thrown into a river.
"The government of the republic profoundly laments these series of events," Mexico's Attorney General Jesús Murillo Karam said. "From day one, we have been in solidarity with the pain of the families and the victims as well as with our responsibility to bring those who did this to justice. We are committed to hand down a punishment that is reasonable within the law, but that also serves as an example and assures that these kinds of crimes are not repeated."
"The case has led to a series of mass protest marches, most recently on Monday, and raised doubts about the rule of law in Mexico. It has helped send President Enrique Peña Nieto's approval ratings plummeting to levels not seen by a Mexican president in two decades.
"The president has promised to revamp local policing and adopt measures to address widespread impunity, but analysts have said he also does not wish a security crisis to define a term that he had hoped would be devoted to improving a slowing economy and buffing Mexico's image.
"In a speech shortly before Mr. Murillo Karam spoke, Mr. Peña Nieto suggested it was time for the nation to move on, even as the public harbors doubts."
On Twitter, Peña Nieto said this conclusion was difficult to accept and that the incident, known in Mexico as Ayotzinapa, for the name of the college, "hurts all of us."
"Ayotzinapa forces us to change," he wrote. "May the pain we've shared inspire us to work toward a just and free Mexico."
Meanwhile, the Mexican newspaper El Universal reports that family members of some of the missing students continued to meet in Iguala, about 120 miles southwest of Mexico City. They heard from the father of one of the victims who was identified by police.
He told them not to lose faith, that there is still hope that the remains will be found and their children could be given a proper burial.