Sorry but the list to that question goes on forever, but I can point out this: If you're dealing with a large number and you want to know if it is divisible, just add up the digits and see if that number is divisible, if you still don't know, repeat the process.
For Example:
684/3=
6+8+4=
18/3=
1+8=
9/3=
3
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the number is divisible by 3 if the sum of the digits in the number is divisible by 3.
Some examples:
3 1212 27
Yes; all numbers that are divisible by 9 are divisible by 3.
All numbers divisible by 3 are NOT divisible by 9. As an example, 6, which is divisible by 3, is not divisible by 9. However, all numbers divisible by 9 are also divisible by 3 because 9 is divisible by 3.
All numbers divisible by 9 are divisible by 3; since 9 = 3 x 3 all multiples of 9 are also multiples of 3. However, all numbers divisible by 3 are not divisible by 9, eg 6 = 2 x 3 but 6 is not divisible by 9 (since 6 is not a multiple of 9) - it only takes one counter example to disprove a theory.
Yes
Even numbers are divisible by 2. Even numbers that are divisible by 3 must be divisible by 2 and by 3, so they have to be divisible by 2 x 3.6, 12, 18, 24 …