What is the remainder when 3 to the power of 2008 divided by 5?

Answer 1

1

Explanation

Note the following:

31=3

32=9

33=27

34=81

35=243

36=729

37=2187

38=6561

You will see that the units digit of the powers of three cycles through the following: 3, 9, 7, 1. 3 raised to a multiple of 4 has 1 as the units digit. Because 2008 is a multiple of 4, 32008 has 1 in the units digit (and is thus the remainder when that number is divided by 5).