Which of the following numbers is a multiple of 8?

### Concept & Strategy The divisibility rule for $8$ states that a number is a multiple of $8$ if the number formed by its last three digits is divisible by $8$. Since $8 = 2^3$, we only need to inspect the final three positions. ### Step-by-Step Solution We will isolate the last three digits of each option and divide them by $8$: * **Option (a) 923872:** Last three digits: $872$ $872 / 8 = 109$. (Perfectly divisible) * **Option (b) 923972:** Last three digits: $972$ $972 / 8 = 121.5$. (Not divisible) * **Option (c) 923862:** Last three digits: $862$ $862 / 8 = 107.75$. (Not divisible) * **Option (d) 923962:** Last three digits: $962$ $962 / 8 = 120.25$. (Not divisible) Only option (a) satisfies the rule. ### Exam Strategy & Shortcut Instead of performing long division on the last three digits, check the hundreds digit. If the hundreds digit is even (like $8$ in $872$), you only need to check if the last two digits ($72$) form a multiple of $8$. Since $72 / 8 = 9$, the number is a multiple of $8$. If the hundreds digit is odd (like $9$ in $972$), add $4$ to the last two digits ($72 + 4 = 76$) and check if that is divisible by $8$. $76$ is not, so it fails. This odd/even trick saves crucial seconds. ### Common Pitfall The most common mistake is confusing the rule for $8$ with the rule for $4$ (last two digits). Test-takers might see $72$ at the end of multiple options and incorrectly assume they all work, leading to confusion or random guessing. ### Final Answer Therefore, the correct answer is **923872**.