### Instruction: Convert $314_{10}$ to base 6.### Response: To convert from base 10 to base 6, I need to repeatedly divide the number by 6 and write down the remainders, starting from the right.
So, $314 \div 6 = 52$ with a remainder of 2.
I write down 2 as the rightmost digit of the base 6 number.
Next, I divide 52 by 6, which gives me 8 with a remainder of 4.
I write down 4 as the next digit to the left.
Then, I divide 8 by 6, which gives me 1 with a remainder of 2.
I write down 2 as the next digit to the left.
Finally, I divide 1 by 6, which gives me 0 with a remainder of 1.
I write down 1 as the leftmost digit of the base 6 number.
So, the base 6 representation of 314 is 1242.