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Master | Next Rank: 500 Posts
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by lokesh r » Thu Sep 09, 2010 6:51 am
Finding units digit of 13^77 is as good as finding units digit of 3^77.

Using famous rule, units digit of

3^1=3,3^2=9,3^3=7,3^4=1,

3^5=3......

77=4x19+1

Units digit of 13^77= Units digit of 3^77=3
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by kmittal82 » Thu Sep 09, 2010 6:59 am
Let list some units digts of 3

3,9,7,1,3,9,...

We see a repetition every 4 intervals (3^1 has same digit at 3^5, 3^2 has same as 3^6 etc..)

Thus, 3^77 will have same as 3^73, which in turn has same as 3^69

77=4x19 + 1, so it will have the units digit of 3^(4+1) = 3^5 = 3
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