how Ancient Egyptians built the outer casing of the pyramid to fit amazingly to each other?

Answer 1

The outer casing which was usually of pink or white granite that was quarried at Aswan and brought to the site on the Nile's annual inundation. As this was the only time of year the river was fast enough and in places deep enough, to float such tremendous loads.
It was first accurately measured into square slabs. Then cut to the correct size and checked by an official and an overseer, before being taken up the ramp that was in place around the pyramid. Measurements of the area were it was to be placed and the exact size of the slab had to match as exactly as possible. This would mean some adjustments may have often required before it was turned onto its side and laid in its place.
It was then the turn of the finishers and stone polishers to file the outer surface level and flat .It would then be polished it to a high shining and lustrous finish.
It is said that even in the time of the Greek visitors, the gleam of the granite facing was dazzling in the sun and made the pyramids difficult to look upon.
No doubt this was the intended effect of the builders.
The pyramids were all completed from the top down. The earthen and shale ramp being removed as each level of the work was totally completed.
Meaning, that by the time they had got to putting on the lower levels of the casing the outside work was almost totally completed.
The outer ramp was taken away and removed to another area and work began on the inside of the pyramid.
The workers were assigned to different teams and competed against each other for extra rations of beer at the end of the working day. Graffiti belonging to teams with names such as "The Might of Horus" have been found.
It required true precision craftsmanship to prepare such hard stone to this fine degree with hand tools,so closely fitting that they required no form of mortar to adhere them to the surface. It was done by the correct level of the pyramids incline.
Working with such reflective material, high up in the hot and brilliant sunlight must have given extra difficulties we can only imagine and wonder at..

Answer 2

They used grinders,
No Idea it is one of the best kept secrets, only the ancient egyptians had this craft even though today we have all this technology to hand we cannot do work like that, go and see Abu Simble they made a pigs ear out of that by reconstructing it
same with Philea Temple. if i could travel through time I would of loved to see how it was done , they say all the stone was split wih fire and water but how did they bore the hole no steel in them days.go and see also the unfinished Obolisk in Aswan where the stone for the Pyramids came from , amazing.
I to could cut and paste on egyptology. but I say what i've seen
and the question is how did they get the stones to fit so perfect??
sand would not polish granite, they use a new invention today called carbide to polish marble granite Etc