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You could combine the tests for divisibility by 3 and 4.
To test for divisibility by three, add all the digits together and see if they're divisible by three. If necessary, you can keep repeating the addition until you come up with a single-digit number.
To test for divisibility by four, take the last two digits. If that two-digit number is divisible by four, then the whole number is. This is because any multiple of 100 is divisible by 4, so only the last two digits matter.
Combined, these two tests will allow you to quickly check for divisibility by 12.
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Can a number be divisible by 6 and 12?
Absolutely - any number that is divisible by 12 - is also divisible by 6 !
Write a rule to determine when a number is divisible by 12?
A number is divisible by 12 if it is divisible by 3 AND it is divisible by 4. Rule 1a (Divisibility by 3): Add up all the digits of the number. Is this number divisible by 3? Rule 1b (Divisibility by 4): Is the number formed by the last two digits of the original number (the number left after deleting the hundreds, thousands, millions etc) divisible by 4? If the answer to 1a is NO, then the number is not divisible by 3 and so not divisible by 12. In this case, obviously, rule 1b is irrelevant. If the answer to 1b is NO, then the number is not divisible by 4 and so not divisible by 12. If the answer to both 1a and 1b is YES, then the number is divisible by 12.
Is 534 divisible by 9?
No. To test: add the digits together and if the sum is divisible by 9, so is the original number. The test can be repeated on the sum until a single digit remains. If this single digit is 9 then the [original] number is divisible by 9, otherwise it gives the remainder when the [original] number is divided by 9. 534 → 5 + 3 + 4 = 12 12 → 1 + 2 = 3 3 ≠ 0 so 12 is not divisible by 9 so 534 is not divisible by 9; the remainder when 534 is divided by 9 is 3.
Is the number 57 prime or composite?
You can see quickly that the number 57 is divisible by 3: 3 * 20 = 60 so if we remove one of those 3's then 3 * 19 = 57 so it is divisible by at least 3 and 19 (as well as itself and 1) Because it is divisible by numbers other than itself and one, 57 cannot be prime. You can also check to see if a number is divisible by 3 by adding its digits and checking to see if that number is divisible by 3: 5+7 = 12 ; and 12 is divisible by 3, so 57 is as well.
What is a number that is divisible by 2 through 12?
Numbers that are divisible by 2 through the number 12 are: 4, 6, 8, 10 and 12.
