Convert 726 to a number in base three

To convert 726 to base three, we need to find the largest power of three that is less than or equal to 726. In this case, 3^6 = 729, which is greater than 726, so we need to use powers of three lower than 729. First, we divide 726 by 243, which is 3^5. The quotient is 2 and the remainder is 240. Next, we divide the remainder 240 by 81, which is 3^4. The quotient is 2 and the remainder is 78. Continuing in this way, we divide 78 by 27, which is 3^3. The quotient is 2 and the remainder is 24. Then, we divide 24 by 9, which is 3^2. The quotient is 2 and the remainder is 6. Finally, we divide 6 by 3, which is 3^1. The quotient is 2 and the remainder is 0. Therefore, the base-three representation of 726 is 222202, which corresponds to the last option (1122).