What is the remainder when \(457 \times 11569\) is divided by 5?

Explanation: The remainder when a number is divided by 5 is the remainder of its unit digit divided by 5. For \(457\), the unit digit is 7. The remainder when 7 is divided by 5 is **2**. For \(11569\), the unit digit is 9. The remainder when 9 is divided by 5 is **4**. The remainder of the product is the remainder of the product of the remainders. Product of remainders = \(2 \times 4 = 8\). The remainder when 8 is divided by 5 is **3**. (The provided solution uses the product of unit digits $7 \times 9 = 63$ and finds $63 \div 5$ remainder $= 3$, which is correct).