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1ExplanationNote the following:31=332=933=2734=8135=24336=72937=218738=6561You 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).
31 divided by 3 is 10 with remainder 1
33 divided by 7 is 4 with remainder 5
40*24 = 960 and 960/40 = 24