Finding Largest 4-Digit Number Divisible by 66

We need to find the largest 4-digit number that can be divided evenly by 66.

Understanding Divisibility Rules

A number is divisible by 66 if it is divisible by both 2 and 33. Since $66 = 6 \times 11$, and 6 and 11 are coprime, the number must be divisible by both 6 and 11. This means it must be divisible by 2, 3, and 11.

Calculation Method

1. Determine the largest 4-digit number: This is 9999.
2. Divide 9999 by 66 to find the remainder.

   $ \frac{9999}{66} $

   Performing the division gives us a quotient and a remainder:

   $ 9999 = 66 \times 151 + 33 $

   The quotient is 151, and the remainder is 33.

3. To find the largest 4-digit number divisible by 66, subtract the remainder from 9999.

   $ \text{Result} = 9999 - \text{Remainder} $

   $ = 9999 - 33 $

   $ = 9966 $

Therefore, the largest 4-digit number completely divisible by 66 is 9966.