It's very easy to test a number to see if it is divisible by 4 or by 9. If it passes both tests, then it is divisible by 4x9=36.
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There is no number, no matter the number of digits, that is only divisible by 2.
Take the number 3336. You know it's divisible by 1 because everything is. You know it's divisible by 2 because it's even. You know it's divisible by 3 because the digits add up to a multiple of 3 and you know it's divisible by 4 because the last two digits are divisible by 4. So you've found at least four factors: 1,2,3 and 4.
Add the digits. If the total is divisible by three, the original number is divisible by three. It's not and it's not.
Double the last digit, subtract it from the rest. If the result is divisible by 7, the whole number is divisible by 7.
No