Why did the Nazis refer to the prisoners as numbers? What other tactics did they use to dehumanize their victims?Wiesel (and other victims of...

These have all been excellent answers.  The purpose behind National Socialism was threefold, one militarist, the second corporate and state identification, and the third (and most important) was racist. The whole idea was to empty acquired territory of "undesirables," ie all who were not sufficiently Germanic in type, according to the pseudo-scientific standards of the Party.  Children "worthy of raising as Germans" were to be adopted by the state, the rest killed with their families.  Young women of sufficiently Germanic type would be bred with SS soldiers.  The land would then be populated  by a "Aryan" people, displacing all else.

The dehumanization began with propaganda against the Jews and others such as fellow traditional social scapegoats the Gypsies, and fringe semi-Protestant groups such as Jehovah's Witnesses.  In the end, dissident Germans, Catholic priests who refused to toe the political line, homosexuals, possible political opponents of Nazism and their relatives ended up in the camps, culminating in families of the old nobility in the aftermath of the von Stauffenburg Plot.  The yellow badges and the ghettos and the concentration camps came early on, then the Death Camps.  These were places like Buchenwald, where there were no great factories for the slave laborers to work, they were simply places where masses of people were shipped and killed.  At Buchenwald, the hospital had no medicines for prisoners, and no treatment was available.  A US Army engineering report by the first allied unit to enter the camp states, "The hospital was a place where moribund prisoners were sent to die."

People had to sleep crowded into bunks which were shelves where as many inmates as possible crowded in with less than a foot and a half space between the tiers.  The prisoners did not receive enough calories per day to survive on a long-term basis.  They were worked mercilessly, and of course many died every day and were sent to the furnaces.  There in most camps the gold teeth, if any, were extracted, the hair, if any, collected for the cushioning inside slippers.  The boneash was sold as fertilizer.  In Buchenwald, the number of prisoners who died in a day was preferably the same as the limits of the furnaces.  If not enough died of starvation, illness and labor the difference was made up by murder, the proper number of prisoners simply hung on meathooks and beaten with bats.

It was Emma Koch, wife of the Commandant of Buchenwald, who began the fad of using the tattooed skin of prisoners as book covers, wall hangings and lampshades.  The dehumanization of the victims of the Nazis began with propaganda and ended in the most dehumanizing and methodical murder factories in all history.  Approximately eleven million died in the camps, about 6 million being Jewish.