### Instruction: When the base-12 integer $1531_{12}$ is divided by $8$, what is the remainder?### Response: I know that base-12 means that each digit represents a power of 12, so $1531_{12} = 1 \cdot 12^3 + 5 \cdot 12^2 + 3 \cdot 12 + 1$.
To divide this by 8, I need to convert it to base-10 first, since I'm more familiar with that.
So, $1531_{12} = 12^3 + 5 \cdot 12^2 + 3 \cdot 12 + 1 = 1728 + 720 + 36 + 1 = 2485$ in base-10.
Now, I can divide 2485 by 8 using long division or a calculator, and I get 310 with a remainder of 5.
So, the remainder is 5 in base-10, but I need to convert it back to base-12 to get the final answer.