Convert the number from decimal form to the given base. 16,691 to base three \( 16,691=\square \) three

We start with the decimal number \( 16691 \) and repeatedly divide by 3, recording the remainder at each step. 1. Divide \(16691\) by 3: \[ 16691 \div 3 = 5563 \quad \text{with remainder } 2. \] 2. Divide \(5563\) by 3: \[ 5563 \div 3 = 1854 \quad \text{with remainder } 1. \] 3. Divide \(1854\) by 3: \[ 1854 \div 3 = 618 \quad \text{with remainder } 0. \] 4. Divide \(618\) by 3: \[ 618 \div 3 = 206 \quad \text{with remainder } 0. \] 5. Divide \(206\) by 3: \[ 206 \div 3 = 68 \quad \text{with remainder } 2. \] 6. Divide \(68\) by 3: \[ 68 \div 3 = 22 \quad \text{with remainder } 2. \] 7. Divide \(22\) by 3: \[ 22 \div 3 = 7 \quad \text{with remainder } 1. \] 8. Divide \(7\) by 3: \[ 7 \div 3 = 2 \quad \text{with remainder } 1. \] 9. Divide \(2\) by 3: \[ 2 \div 3 = 0 \quad \text{with remainder } 2. \] Now, list the remainders in reverse order (from the last division to the first): \[ 2,\; 1,\; 1,\; 2,\; 2,\; 0,\; 0,\; 1,\; 2. \] Thus, the base three representation is \[ 16691 = 211220012 \text{ (base three)}. \]