The stricken group were amongst a party of more than 30 others from Leeds University Hiking Club who had travelled to the Highlands for a weekend's climbing.
Police are still trying to piece together what led to the latest fatality in Scotland's mountains.
A family member confirmed the dead climber is Graham Connell, 31, from Castleford, West Yorkshire. According to the relative who spoke about the tragedy on Twitter, he was a former student who had returned to the mountains with the university club.
The climbers first ran into trouble on Sunday afternoon, when one of a party of seven men suffered a fall in the Northern Corries area of the range.
He was not seriously injured but mountain rescuers assisted him off the hill.
The rest of the party were later caught in horrendous blizzard conditions, and are understood to have become disorientated.
A major search operation involving 112 police staff, RAF and mountain rescue teams was launched on Sunday evening when the six men were reported overdue.
Police received a call from the group and the Braemar Mountain Rescue Team then located five of the party on Carn Tarsuinn at around midday yesterday. They were not hurt and were lifted to safety by an RAF Lossiemouth helicopter.
Shortly afterwards, the sixth man's body was found in the Jacob's Ladder area, a gully in Coire an t-Sneachda, which is several miles from where the others were found.
Chief Inspector Colin Gough, based at Northern Constabulary in Aviemore, said he still wanted to speak to the survivors to establish what happened and why they were so far apart.
Leeds University Hiking Club's website advertised the trip to the Cairngorms, which left the students' union in Leeds at 5.15pm on Friday
A message said: "It is a long drive to Scotland so please don't make us wait for you.
"Bring all of your gear to put in the van, as well as some spare warm clothes for the minibus and some food for your dinner/money to buy something at a service station. Remember: Scotland will be cold.
"You will need more clothes than you normally do. You will need more food than you normally do (statistic – you can burn up to 5000 calories in winter conditions). Please make sure you have enough for both or all three days, depending on how long you're coming for."
The Saturday itinerary added: "This will not only be our first day of walking but in the evening we will be going to a presentation given by Cairngorms Mountain Rescue Team, coincidentally by an ex-club president.
"Sunday – more winter hiking. Some keen hikers who value their degrees will be heading back to Leeds on Sunday evening to make it in for lectures on Monday.
"Well done to them all.
"Monday – The rest of us will be on our third day of winter epicness. We will head back to Leeds on Monday evening, most likely arriving quite late – be prepared to be a bit bleary-eyed on Tuesday morning."
The latest incident is the sixth death in Scotland's mountains in 2013, following the four lives lost in the Glencoe avalanche three weeks ago and the loss of a climber on Ben Nevis a week later.
This latest search involved over 100 people and was co- ordinated by Northern Constabulary and Cairngorm Mountain Rescue Team, with assistance from Braemar and Dundonnell mountain rescue teams and officers from the Police Service of Northern Ireland in the area on a training exercise.
Further help was given by mountain rescue team members from the Lake District and Ogwen Valley in Wales, as well as sniffer dogs.
Meanwhile, the RAF sent mountain rescue personnel from RAF stations in Lossiemouth, Leuchars and Leeming.
Police inquiries into the incident are continuing and a report will be submitted to procurator fiscal.