Add the digits. If the total is divisible by three, the original number is divisible by three. It's not and it's not.
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3 is not divisible by 126. 126 is divisible by 3.
3 is not divisible by 72. 72 is divisible by 3.
512 is not divisible by 3.
Take the number 3336. You know it's divisible by 1 because everything is. You know it's divisible by 2 because it's even. You know it's divisible by 3 because the digits add up to a multiple of 3 and you know it's divisible by 4 because the last two digits are divisible by 4. So you've found at least four factors: 1,2,3 and 4.
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.