You don't even have to get that cute. Do integer division, multiply the result by the divisor, and subtract the product from the original dividend. Surely you can't say you don't use multiplication, division, and subtraction.
highly recommend learning how division works within assembly. If you can understand sending this data into registers, you will never forget how mod works. Honestly, I dont even care if you use modulus or not. Solve the problem within a function demonstrating you know CS101 concepts we are good. like, really. No judgement, this is just an idiot filter.