Divisibility if a number by 3 is not determined by its last digits: instead it is determined by the number's digital root.
You get the digital root of a number by adding together all its digits. If the answer is a big number, then find the digital root of the answer. Keep going until you have a number that is smaller than 10. If this number is 3, 6 or 9 (all divisible by 3) then the original number is divisible by 3. And it not, it is not.
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The last digits don't tell you whether the entire number is divisible by 3.
The number is divisible by 3 if ALL of its digits ADD UP to a multiple of 3 .
All whole numbers are divisible by 1. Numbers are divisible by 2 if they end in 2, 4, 6, 8 or 0. Numbers are divisible by 3 if the sum of their digits is divisible by 3. Numbers are divisible by 4 if the last two digits of the number are divisible by 4. Numbers are divisible by 5 if the last digit of the number is either 5 or 0. Numbers are divisible by 6 if they are divisible by 2 and 3. Numbers are divisible by 9 if the sum of their digits is equal to 9 or a multiple of 9. Numbers are divisible by 10 if the last digit of the number is 0.
Even numbers are divisible by 2. Even numbers that are divisible by 3 must be divisible by 2 and by 3, so they have to be divisible by 2 x 3.6, 12, 18, 24 …
For 4:Are the last two digits in your number divisible by 4? If so, the number is too! For example: 358912 ends in 12 which is divisible by 4, thus so is 358912. For 6: The number must be divisible by 2 and 3. For 8: This one's not as easy, if the last 3 digits are divisible by 8, so is the entire number. Example: 6008 - The last 3 digits are divisible by 8, therefore, so is 6008.
For starters, the number 3 is divisible by 3 but not by 2. Next, 9, 27 etc. All the odd multiples of 3 are divisible by 3 but not 2. So there is an infinite number of numbers that are divisible by 3 and not 2.
All 4 digit numbers that are divisible by 9 are also divisible by 3. The first is 1008 and the last is 9999.