You can break it up into parts. If the parts are divisible by three, you can assume that the whole number is also divisible by three and check it.
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Yes, if x is an integer divisible by 3, then x^2 is also divisible by 3. This is because for any integer x, x^2 will also be divisible by 3 if x is divisible by 3. This can be proven using the property that the square of any integer divisible by 3 will also be 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.
Not evenly. A number is divisible by 3 if the sum of its digits is divisible by 3.
416 is divisible by 2 but is not divisible by 3.
No. To be divisible by 6, a number must be even (divisible by 2) and divisible by 3. Although 3058 is even, it is not divisible by 3 since 3+0+5+8 = 16 which is not divisible by 3. Thus is it not divisible by 6.