The file is binary and having elements as "0" and "1". By Finite Field theory, the element '0' is an additive identity, and '1' is a multiplicative identity.
If you want to compress, use source coding algorithms such as Run length.
Division for compression , sorry I have not come across . Now division in CRC (cyclic redundancy code) yes it is based on long division . Here the remainder is used for error checks and correction.
Secondly , in machine level or otherwise we should never divide # of bits in the dividend being equal to divisor (like how you have shown) .
It is a thumb rule: The # on bits in the dividend should be @ least two times the length of the divisor .
(111111 101010)/101010 = xxxxxx xxxxxx , where the ones are sign extension and the quotient (xxxx ....)is of a particular sign ( 2's complement )
So yes it is not numerical division or multiplication per se ...
Coding or compressing by division will not yield the compression or reduction memory indeed even after performing computationally intensive steps operations, we will have another set of code words which may require a nearby memory as required by the original file. Also, the key you select and the content will effect the actual result. Also, there will be an uncertainty on deciding the key with which you will perform the division, for each file.
Yes, except that it is a mathematical correctness, so I thought that it could be used in some way in computing, because if you divide the code by code, it would contain less information that would contain more information. Bit is not the smallest unit of information. I base myself on the textbook of cybernetics. It would be an oversight, but it should be less weight.