### Instruction: What is the base four equivalent of $123_{10}$?### Response: To convert a number from base ten to base four, I need to repeatedly divide by four and write down the remainders.
So, starting with $123_{10}$, I divide by four and get $30$ with a remainder of $3$.
I write down the $3$ as the rightmost digit of the base four number.
Then I divide $30$ by four and get $7$ with a remainder of $2$.
I write down the $2$ as the next digit of the base four number, to the left of the $3$.
Then I divide $7$ by four and get $1$ with a remainder of $3$.
I write down the $3$ as the next digit of the base four number, to the left of the $2$.
Finally, I divide $1$ by four and get $0$ with a remainder of $1$.
I write down the $1$ as the leftmost digit of the base four number.