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mangomangodolly
- Junior | Next Rank: 30 Posts
- Posts: 13
- Joined: Sun Nov 25, 2012 1:30 am
This problem can be easily solved by remembering the blue colored fact.
14^40 = (2*7)^40 = (2^40)*(7^40)
Now, 7^4 = 2401. Hence, 7^4 raised to any power will end in ...01.
Hence, last two digits of 7^40 = (7^4)^10 is 01.
And, 2^10 = 1024
24 raised to any odd power ends with 24 and 24 raised to any even power ends with 76. This is because 24^2 ends with 76 and 76 raised to any power always ends 76.
Hence, 2^40 = (2^10)^4 ends with 76.
Hence, last two digits of 14640 is last two digits of 76*01 = 76
