If you notice that 340 is close to $ 7^3=343=1000_7 $, then it makes the problem much easier. Since $ 343=1000_7 $, that makes $ 342=666_7 $, or the largest three-digit number in base 7. To get 340, we subtract 2, which means subtracting 2 from the digit in the $ 7^0 $ place. That leaves us with $ \boxed{664_7} $. Alternatively, the largest power of 7 less than 340 is $ 7^2=49 $, and the largest multiple of 49 less than 340 is $ 6\cdot49=294 $. That means there is a 6 in the $ 7^2 $ place. We have $ 340-294=46 $ left, which can be represented as $ 6\cdot7^1+4\cdot7^0 $. So, we get $ 340=6\cdot7^2+6\cdot7^1+4\cdot7^0=\boxed{664_7} $.