### Instruction: What is the base four equivalent of $123_{10}$?### Response: To convert a base ten number to base four, I need to repeatedly divide by four and keep track of the remainders.
So I start with 123 and divide by four.
I get a quotient of 30 and a remainder of 3.
I write down the remainder as the rightmost digit of my base four number, so far it's just 3.
Then I divide 30 by four.
I get a quotient of 7 and a remainder of 2.
I write down the remainder as the next digit of my base four number, so now it's 23.
Then I divide 7 by four.
I get a quotient of 1 and a remainder of 3.
I write down the remainder as the next digit of my base four number, so now it's 323.
Finally, I divide 1 by four.
I get a quotient of 0 and a remainder of 1.
I write down the remainder as the leftmost digit of my base four number, so now it's 1323.
This is the base four equivalent of 123 in base ten.