What is the largest four-digit number that is exactly divisible by 88?

Concept / Approach

• The largest four-digit number is 9999. To find the largest number divisible by 88 not exceeding 9999, compute floor(9999 ÷ 88) and multiply back by 88.

Step-by-step calculation9999 ÷ 88 = 113.625…Largest integer ≤ 113.625 is 113Required multiple = 113 × 88 = 9944

Quick check88 × 114 = 10032 > 9999, so 9944 is indeed the greatest four-digit multiple.

Common pitfallDo not round 113.625 up to 114; we must take the floor to stay ≤ 9999.

Final Answer9944