Is the number $4832718$ divisible by $11$?

### Concept & Logic The divisibility rule for $11$ states that a number is divisible by $11$ if the difference between the sum of its digits at odd positions and the sum of its digits at even positions is either $0$ or a multiple of $11$. ### Step-by-Step Solution **Given:** The number to evaluate is $4832718$. **Calculation:** Step 1: Calculate the sum of digits at odd places (starting from the rightmost digit). Odd places (1st, 3rd, 5th, 7th): $8 + 7 + 3 + 4 = 22$ Step 2: Calculate the sum of digits at even places. Even places (2nd, 4th, 6th): $1 + 2 + 8 = 11$ Step 3: Find the difference between these two sums. $$ 22 - 11 = 11 $$ Since the difference is $11$, which is a multiple of $11$, the entire number is divisible by $11$. ### Exam Strategy & Shortcut Instead of summing them separately, you can pair adjacent digits and find their differences, then sum those differences. For $4832718$: $(4-8) + (3-2) + (7-1) + 8 = -4 + 1 + 6 + 8 = 11$. Since $11$ is divisible by $11$, the number is divisible. This method keeps the numbers much smaller during mental calculation. ### Common Pitfall A frequent error is miscounting the positions (even/odd) or simply adding all the digits together, confusing the rule of $11$ with the rule of $3$ or $9$. ### Final Answer Therefore, the correct answer is **Yes, it is divisible by 11**.