A number is divisible by 3 if the sum of its digits is divisible by 3. You check the sum, not the original number.
Example: Is 12345 divisible by 3? Add digits: 1 + 2 + 3 + 4 + 5 = 15. Is 15 divisible by 3? Yes (15 = 3 × 5). So 12345 is divisible by 3.
If the sum is large, repeat the process. For 15: 1 + 5 = 6, which is divisible by 3.