[AnotherGoodName]

To dive into this a bit more without using too much math jargon, under modulo every integer division is a trivial integer multiplication but the number you multiply by has to figured out before hand.

The above is also not true of factors of the modulo itself but then that's just a right shift so that part is easy.

eg. Under mod 35 if i want to divide by 3 i can just multiply by 12 since 12x3 = 1 under mod 35.

eg2. Under mod 35 if i want to divide by 11 i can just multiply by 16 since 16x11 = 1 under mod 35.

I can do this for any number that doesn't share factors with 35 since there's always a multiple to that number that will give 1. I could also create base 2 examples similarly. It's called the multiplicative inverse.

[ridiculous_fish]

To clarify, there are two separate notions of division-as-multiplication discussed here.

Modular division is straightforward to convert to a multiplication; however this is mainly for specialized applications, like cryptography and number theory. It's uncommon to want divide-by-2 to make the value larger.

Ordinary flooring division can also be converted to a multiplication problem when the dividend is bounded. This uses the "magic number" approach where you multiply by a rounded scaled reciprocal, and then do some work to correct the error from rounding.