More details about look-up table in ROM: ROM is a memory device with constant numbers stored in it. It has an address input bus and a data output bus.
Example of ROM with look-up table for dividing numbers 0 to 7:
Address Data
------- ----
0 . . . 0
1 . . . 0
2 . . . 1
3 . . . 1
4 . . . 1
5 . . . 2
6 . . . 2
7 . . . 2
The above is good enough for a 3 bit integer. Connect the number you want to divide by 3 to the address bus, and get the result from the data bus (rounded to the nearest integer).
If your data path is 8 bit, it is still practical to use a single look-up table ROM: the ROM size would be 256 bytes. For 32 bit it not practical to use a single ROM, so you'll have to split the number, as suggested by lostinxlation.