What is the first digit (from left to right) of the base $8$ representation of $473_{10}$?
One way to do this is to repeatedly divide by $8$ and write down the remainders. So, $473 \div 8 = 59$ with a remainder of $1$. Then, $59 \div 8 = 7$ with a remainder of $3$. Finally, $7 \div 8 = 0$ with a remainder of $7$. So, the base $8$ representation of $473_{10}$ is $731_8$, where the subscripts indicate the base. The first digit of this representation is $7$. 