If the digits add up to a multiple of three
for example:
52039
5+2+0+3+9=19
19 is not divisible by 3 so 52039 is not divisible by 3
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342
3+4+2=9
9 is divisible by 3 so 342 is divisible by 3
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what is divisible by two,three,four,five and ten
5, 7, a bunch of numbers that are odd are not divisible by 3. numbers that are divisible by three can have all their numbers added together and come out with a number that is divisible by 3.
The smallest three-digit number divisible by the first three prime numbers (2, 3, and 5) and the first three composite numbers (4, 6, and 8) is 120.
There are eight pairs of numbers divisible by three that sum to 150, and 75 is also divisible by three, so: sum = 17 * 75 = 750 + 525 = 1275
The sum of three consecutive odd numbers must be divisible by 3. As 59 is not wholly divisible by 3 the question is invalid. PROOF : Let the numbers be n - 2, n and n + 2. Then the sum is 3n which is divisible by 3. If the question refers to three consecutive numbers then a similar proof shows that the sum of these three numbers is also divisible by 3. Again, the question would be invalid.