What largest 3 - digit number divisible by both 6 and 9?

Answer 1

999 is divisible by 9, but not by six; the next lower number divisible by 9 is 990, which is also divisible by 6, so that's the answer.

Some shortcuts for divisibility:

0 is divisible by any number.

If the last digit of a number is divisible by 2, the number itself is divisible by 2.

If the sum of the digits of a number is divisible by 3, the number itself is divisible by 3.

If the last TWO digits of a number are divisible by 4, the number itself is divisible by 4.

If the last digit of a number is divisible by 5, the number itself is divisible by 5.

If a number is divisible by both 2 and 3, it is divisible by 6.

If the last THREE digits of a number are divisible by 8, the number itself is divisible by 8.

If the sum of the digits of a number is divisible by 9, the number itself is divisible by 9.

990: 9+9+0=18, which is divisible by 9, so 990 is divisible by 9.

18 is also divisible by 3, so 990 is divisible by 3, and since 990 ends in 0 it's also divisible by 2, meaning that it's divisible by 6 as well.