All multiples of three, which is an infinite number, including 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 . . .
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If the sum of the individual digits in the number is divisible by 3,
then the whole number is divisible by 3.
Weird, but convenient.
Not all even numbers are divisible by 6. These numbers are not evenly divisible by 6: Any number smaller than 6. Any number not divisible by 3. If a number is divisible by both 2 and 3, it is divisible by 6.
Prime numbers are only divisible by 1 and themselves. Since 3 is not a prime number, any prime number divisible by 3 does not exist. Therefore, the set of prime numbers divisible by 3 is an empty set.
Many odd numbers are divisible by 3. 3 itself for example, as well as 9, 15, 21, 27, ... Being odd and being divisible by three are not related.
All multiples of 6 Numbers are evenly divisible by 6 if they are evenly divisible by both 2 AND 3. Even numbers are always evenly divisible by 2. Numbers are evenly divisible by 3 if the sum of all the individual digits is evenly divisible by 3. For example, the sum of the digits for the number 3627 is 18, which is evenly divisible by 3 but 3627 is an odd number so the number 3627 is not evenly divisible by 6
Clearly, both 810 and 910 are divisible by 5. A wee trick regarding numbers that are a multiple of 3, is that the component numbers, when added together, are divisible by three. So, 654 is divisible by 3, as 6+5+4 = 15 which is divisible by 3. In your example, 810 components add up to 9, which is divisible by 3. But the components of 910 add up to 10 which is not so divisible.