Find the largest 4 digit number that is exactly divisible by 66.

9966

For a number to be completely divisible by 66, it has to be divisible by 6 and 11

Following are the divisibility rules:

Pick the largest number from the options:

9987 - is not divisible by 6, as it means the number must be divisible by 2 and 3 and the number is not divisible by 2(unit digit is odd)

Pick the next number i.e., 9966- it is divisible by both 6 and 11 thus, it is the correct answer. Divisibility rules of 11 says that the difference between the sum of alternate numbers must be 0 or divisible by 11.

15 - 15 = 0, thus divisible by 11