The largest 4 digit number exactly divisible by 88 is: Options : 9988 8888 9944 none

Break Down the Problem

1. Identify the largest 4-digit number, which is 9999.
2. Determine the largest 4-digit number that is divisible by 88 by finding the largest multiple of 88 that is less than or equal to 9999.

Relevant Concepts

To find the largest number divisible by 88:

• Use the formula: $\text{Largest divisible number} = \left\lfloor \frac{\text{largest number}}{\text{divisor}} \right\rfloor \times \text{divisor}$

Analysis and Detail

1. Calculate $\left\lfloor \frac{9999}{88} \right\rfloor$: $\frac{9999}{88} \approx 113.3841$ Taking the floor value, we have: $\left\lfloor 113.3841 \right\rfloor = 113$

2. Now, multiply by 88: $113 \times 88 = 9944$

Verify and Summarize

To verify, check if 9944 is less than 9999 and if it is divisible by 88:

• $9944 \div 88 = 113$ exactly, confirming divisibility.

Final Answer

The largest 4-digit number exactly divisible by 88 is 9944.