What is the last digit of the base $6$ representation of the base ten integer $355$?
To convert a number from base ten to base six, I need to repeatedly divide by six and write down the remainders until I reach zero. The last digit of the base six representation will be the first remainder I get. So I start by dividing $355$ by $6$. I can use long division or a calculator to find that $355 \div 6 = 59$ with a remainder of $1$. That means the last digit of the base six representation is $1$. 