What is the last digit of $7^{2015}$?

Question

What is the last digit of $7^{2015}$?

Answer 1

Hint:

Consider $7^1, 7^2, 7^3, \ldots$.

The last digit of this series cycles through 7, 9, 3, 1, 7, and repeats thus.

We can see that it goes through four different last digits.

Now consider 2015 modulo 4.