elementary number theory - Calculate the last digit of $3^{347}$

I think i know how to solve it but is that the best way? Is there a better way (using number theory).

What i do is:
knowing that

1st power last digit: 3
2nd power last digit: 9
3rd power last digit: 7
4rh power last digit: 1
5th power last digit: 3

$3^{347} = 3^{5\cdot69+2} = (3^5)^{69} \cdot3^2 = 3\cdot3^2=3^3=27$ so the result is $7$.

Answer

How about
$$3^2 \equiv -1\pmod {10}$$
so
$$3^{347} \equiv 3^{2\cdot 173+1} \equiv 3 \cdot(-1)^{173} \equiv -3 \equiv 7 \pmod {10}$$