Yes, yes, and no.
3- sum of digits must be multiple of 3.
6- sum of digits must be multiple of 3 and number must be even (multiple of 2).
9- sum of digits must be multiple of 9.
(The sum of the digits here is 21.)
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To determine which number is divisible by 3, 6, and 9, we need to check if the sum of the digits of each number is divisible by 3. For 369: 3+6+9 = 18, which is divisible by 3, 6, and 9. Therefore, 369 is divisible by 3, 6, and 9. For 246: 2+4+6 = 12, which is divisible by 3 but not by 6 or 9. Therefore, 246 is divisible by 3 but not by 6 or 9. For 468: 4+6+8 = 18, which is divisible by 3, 6, and 9. Therefore, 468 is divisible by 3, 6, and 9. For 429: 4+2+9 = 15, which is divisible by 3 but not by 6 or 9. Therefore, 429 is divisible by 3 but not by 6 or 9. Therefore, the numbers 369 and 468 are divisible by 3, 6, and 9.
72,344 is not evenly divisible by 3 or by 6 or by 9.
42 is divisible by 2, 3 and 6 but not by 9.
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.
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.