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