How to prove that every power of 6 ends in 6? Yesterday I had the traditional math matriculation exam, and in it there was a question "In what digit does the number $2016^{2016}$ end in?" After the test The Matriculation Examination Board published a pdf in which they show how to basically solve all the problems in the test, and for the aforementioned question the solution was "Because every power of 6 ends in 6, so does every power of 2016, and thus the last digit is 6". I understand everything else in that problem now, except how to actually show that every power of 6 ends in 6. From there on I know how to solve the last digit if $2016^{2016}$. So,

how to prove that every power of 6 ends in 6?


A little hint: $6*6\bmod 10 = 6$.
