the largest 4 digit number exactly divisible by 88
The largest 4 digit number exactly divisible by 88
Answer: To find the largest 4-digit number that is exactly divisible by 88, we need to focus on two main factors: the range of 4-digit numbers and the divisibility rule of 88.
Since a 4-digit number has a range between 1000 and 9999, we look for the maximum number within this range that is divisible by 88.
To determine if a number is divisible by 88, it must be divisible by both 8 and 11. To be divisible by 8, the last three digits of the number must form a multiple of 8. To be divisible by 11, the alternating sum of the digits must be divisible by 11. Therefore, a number that satisfies both of these conditions will be divisible by 88.
Starting from the highest 4-digit number, which is 9999, we work our way down to find the largest 4-digit number that meets the criteria. After some calculation, we find that 9824 is the largest 4-digit number that is exactly divisible by 88.
So, @LectureNotes was correct in identifying 9824 as the largest 4-digit number exactly divisible by 88.