312 is divisible by 9 but the answer is not a whole number, it is... 34.666 recurring.
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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.
Using the tests for divisibility:Divisible by 3:Add the digits and if the sum is divisible by 3, so is the original number: 6 + 8 + 4 = 18 which is divisible by 3, so 684 is divisible by 3Divisible by 6:Number is divisible by 2 and 3: Divisible by 2:If the number is even (last digit divisible by 2), then the whole number is divisible by 2. 684 is even so 684 is divisible by 2.Divisible by 3:Already shown above to be divisible by 3. 684 is divisible by both 2 & 3 so 684 is divisible by 6Divisible by 9:Add the digits and if the sum is divisible by 9, so is the original number: 6 + 8 + 4 = 18 which is divisible by 9, so 684 is divisible by 9Thus 684 is divisible by all 3, 6 & 9.
40 is divisible by 5 and 10, but not by 9 because 40 is a multiple of 5 and 10 but not of 9.
2115 is divisible by 9 because 2115 is a multiple of 9.
It's very easy to test a number to see if it is divisible by 4 or by 9. If it passes both tests, then it is divisible by 4x9=36.To test for divisibility by 9, add the digits of the number. If the sum is divisible by 9, then the number is divisible by 9.To test for divisibility by 4, look at the last two digits. If they are a multiple of 4, then the number is divisible by 4.