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Question 265435: What is the one’s digit of the number 7^2005?
Answer by vksarvepalli(154)   (Show Source):
You can put this solution on YOUR website! to get the unit's digit of 7^2005
first we need to observe the pattern of the powers of 7
7^1 = 7 units digit is 7
7^2 = 49 (7*7) units digit is 9
7^3 = 243 (9*7) units digit is 3
7^4 = ---1 (3*7) units digit is 1
7^5 = ---7 (1*7) units digit is 7
again the sequence repeats
the sequence is 7,9,3,1
now for 7^2005 the power 2005 can be written as (4*501)+1
so 501 cycles will be completed
that means 7^2004 will end in 1
and for 2005 again the sequence starts and the units digit will be 7
so the one’s digit of the number 7^2005 is 7. (Answer)
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