Using the tests for divisibility:
6 + 8 + 4 = 18 which is divisible by 3, so 684 is divisible by 3
684 is even so 684 is divisible by 2.
684 is divisible by both 2 & 3 so 684 is divisible by 6
6 + 8 + 4 = 18 which is divisible by 9, so 684 is divisible by 9
Thus 684 is divisible by all 3, 6 & 9.
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Multiples of 9 and 6 are also divisible by three, the reverse is not true. 15 is divisible by 3, but not 6 or 9. 27 is divisible by 3 and 9, but not 6. 12 is divisible by 3 and 6, but not 9. 54 is divisible by 3, 6 and 9.
The Greatest Common Factor of 9, 36, 72: 9
18
Yes to both.
6