Implementing Integer Division in hardware
A nice approach is to start with the dividend in a register whose width equals the combined widths of the divisor and intended quotient.  Then repeatedly compare the upper portion of that register against the divisor.  If it's greater than or equal, subtract the divisor and shift the register left, putting a "1" in the LSB.  If it's less, shift left, putting a "0" in the LSB.  Iterate that once for each bit of the quotient.  The lower part of the dividend register will be left holding the quotient, while the upper part will be left holding the remainder.

Depending upon how exactly you do things, it may be necessary to handle the first or last iteration specially, but the above approach is pretty straightforward.