If you don't know about modulus, you don't have to re-implement it. For Fizzbuzz you're looping anyway, so you can just maintain two counters, one that counts to 3 and resets, and one that counts to 5 and resets. When one of the counters resets, you know the main loop counter is a multiple of 3 or 5. Like so:

    def fizzbuzz_no_modulo():
        counter_three = 1
        counter_five = 1
        for i in range(1, 101):
            output = []
            if counter_three == 3:
                output.append('Fizz')
                counter_three = 0
            if counter_five == 5:
                output.append('Buzz')
                counter_five = 0
            if not output:
                output.append(str(i))
            print(''.join(output))
            counter_three += 1
            counter_five += 1