Power of 2 - Part 1

Note that the units digits of powers of two repeat modulo four in the sequence (2, 4, 8, 6). Since 2014 is 2 modulo 4, the answer is the second number in the sequence, which is 4.

Do 2 to the power 1,2,3,4,5…. until you find a pattern. The pattern is 2,4,8,6,2,4,6,8 in the units digit. Then divide 4 (the number of digits till the pattern repeats) into 2014. Which gives you a remainder of 2, and the second repeating digit is 4 so the remainder is 4 (since any number divided by ten will give the remainder of the units digit). So the answer is…. 4!

Same as asking for the last digit of 2^2014. You can do it by two methods, though logic of both the methods are more or less same. Either find a pattern between the last digits of 2 which is (2,4,8,6,2,4,6,8...) so you can see that after a certain interval of time, the digits are repeating themselves. Proceed like that to find the unit place digit of 2^2014, or use modulo function. See what the remainder is when 2^2014 is divided by 10.

2014 /2=1007 , (2^2)=4 then (2^2)^1007 unique digit =4 and 4/10 remainder=4

2^1 mod 10 = 2 2^2 mod 10 = 4 2^3 mod 10 = 8 2^4 mod 10 = 6 and then the sequence repeats :) 2^2012 will be one end of one such set so 2^2013 mod 10 = 2 again & 2^2013 mod 10 = 4!!

2^2014 / 5 = 1^2014 /5 so 2014/5 = 402 and reminder is 4