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I have two excel workbooks each of which has huge amount of rows (in lakhs).
With such a large number of rows, anything matters, and excel may not be the best tool for this problem.
Excel is very nice, but it is at expense of speed. Database like SQL will handle you data in a more efficient fashion.
Sorting the data have a huge impact on performance.
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I have tried vlookup, index-match, only match.
I have found a solution that suggests using partial match with 2 vlookups but that does not help either.
I have tried conditional formatting as well in which case the filtering is taking a lot of time.
The exact formulas you used and the data matters. Not every formula work with every data, and some combinations are more efficient than others.
Without details on what you have done, it is impossible to give you better advices than those generalities. And teaching you databases is out of scope of this forum.