Find the smallest number of five digits which is exactly divisible by 476.

### Concept & Logic To find the smallest $N$-digit number divisible by a given divisor, start with the absolute smallest possible $N$-digit base number. Treat it as an addition problem because subtracting anything from the smallest $N$-digit number would reduce it to $N-1$ digits. ### Step-by-Step Solution - **Given:** Find the smallest 5-digit number divisible by 476. - **Calculation / Deduction:** The absolute smallest 5-digit number is 10000. - Divide 10000 by 476 to determine the remainder. - $10000 \div 476$ yields a quotient of 21 and a remainder of 4. - Since we cannot subtract (which would yield a 4-digit number like 9996), we must add to reach the next multiple. - Number to add = $\text{Divisor} - \text{Remainder} = 476 - 4 = 472$. - Add this value to the base number: $10000 + 472 = 10472$. ### Exam Strategy & Shortcut Always write down the base number (like 10000) and immediately find the remainder. Apply the standard formula for finding the next multiple: $\text{Base} + (\text{Divisor} - \text{Remainder})$. Never use subtraction for smallest N-digit constraint questions. ### Common Pitfall Students often subtract the remainder (4) from 10000 to get 9996. While 9996 is perfectly divisible by 476, it is only a 4-digit number, thereby failing the primary constraint of the question. ### Final Answer Therefore, the correct answer is 10472.