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

Introduction:
This is a standard divisibility and multiples problem. You are asked to find the largest four-digit integer that is exactly divisible by 88. Such questions appear frequently in aptitude tests to check your comfort with division and multiples.

Given Data / Assumptions:

• We consider only four-digit numbers, that is numbers from 1000 to 9999.
• We want the largest four-digit number N such that N is divisible by 88.
• Divisible by 88 means N = 88 × k for some integer k.

Concept / Approach:
To get the largest four-digit multiple of 88, we divide the largest four-digit number 9999 by 88 and take the integer part of the quotient. Then we multiply 88 by this quotient to obtain the required multiple.

Step-by-Step Solution:
Step 1: Start from the upper limit 9999.Step 2: Divide 9999 by 88 to get the approximate quotient.88 * 100 = 8800 (still four digits).88 * 110 = 9680.88 * 113 = 88 * (100 + 13) = 8800 + 1144 = 9944.88 * 114 = 88 * (100 + 14) = 8800 + 1232 = 10032 (which is five digits).Step 3: Conclude.The last product still under 10000 is 88 * 113 = 9944.

Verification / Alternative check:
Check that 9944 is divisible by 88 using quick division: 9944 ÷ 88 = 113 exactly, with no remainder. Also, the next multiple 9944 + 88 = 10032, which exceeds 9999, so 9944 is indeed the largest four-digit multiple.

Why Other Options Are Wrong:
8888 is divisible by 88 but is smaller than 9944. 9999 and 9988 are not exact multiples of 88. 9680 is also a multiple of 88 but smaller than 9944. So only 9944 satisfies both conditions: four-digit and largest possible.

Common Pitfalls:
Some learners try to test each option with long division, which is time-consuming. Others mistakenly choose 9999 or 9988 just because they look large. Always use multiplication or division systematically to identify the correct multiple.

Final Answer:
The largest four-digit number exactly divisible by 88 is 9944.