1. The problem is to solve the expression $289 \times 125 \mod 27$. 2. We use the modular arithmetic property: $ (a \times b) \mod m = [(a \mod m) \times (b \mod m)] \mod m $. 3. First, find $289 \mod 27$: $$289 \div 27 = 10 \text{ remainder } 19 \implies 289 \mod 27 = 19$$ 4. Next, find $125 \mod 27$: $$125 \div 27 = 4 \text{ remainder } 17 \implies 125 \mod 27 = 17$$ 5. Now multiply the remainders: $$19 \times 17 = 323$$ 6. Finally, find $323 \mod 27$: $$323 \div 27 = 11 \text{ remainder } 26 \implies 323 \mod 27 = 26$$ 7. Therefore, the answer is: $$289 \times 125 \mod 27 = 26$$