There is no limit to the number of digits.
If, for example, a X is a k-digit number which is divisible by 4 then 10*X is divisible by 4 and 10*X will be a (k+1)-digit number.
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The greatest 4-digit number that is divisible by 16 is 9984
There is no 4-digit number that is divisible by zero.
9960
9996
999996