A group of $8$ pirates agree to divide a treasure chest of gold coins among themselves as follows. The $k^{th}$ pirate to take a share takes $\frac{k}{8}$ of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for which this arrangement will allow each pirate to receive a positive whole number of coins. How many coins does the $8^{th}$ pirate receive?