1. The problem asks to convert the decimal number 314 (base 10) to base 6. 2. A base (or radix) is the number of unique digits, including zero, used to represent numbers in a positional numeral system. For example, base 10 uses digits 0-9, base 6 uses digits 0-5. 3. To convert from base 10 to base 6, repeatedly divide the number by 6 and record the remainders. 4. Start with 314:\ 314 \div 6 = 52 \text{ remainder } 2 5. Next, divide 52 by 6:\ 52 \div 6 = 8 \text{ remainder } 4 6. Then divide 8 by 6:\ 8 \div 6 = 1 \text{ remainder } 2 7. Finally, divide 1 by 6:\ 1 \div 6 = 0 \text{ remainder } 1 8. Collect the remainders from last to first: 1 2 4 2 9. Therefore, $$314_{10} = 1242_6$$ in base 6. This means the number 314 in decimal is represented as 1242 in base 6.