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.
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
9990
The greatest 4-digit number that is divisible by 16 is 9984
There is no 4-digit number that is divisible by zero.
99996
9960
9996
9990
9996
9990
999996
The largest 4 digit number that is divisable by 1 2 3 and 4 is........9996
It is 9996
The greatest 4 digit integer divisible by 3 (and therefore a multiple of 3) is 9999.