Part $1$: Coding task $$ One task, two levels

Regular Level Task for $100$ points: Write two short assembly subroutines: one that does $16-$

bit integer division with remainder, and one that factorizes $16-$bit semiprimes.

A semiprime is simply a number that is the product of exactly two prime numbers, e$.$g$.,15=3*5,$

$21=3*7,$ etc. Knowing that there are exactly two prime factors makes the program $($or the data

structures that are required to record the factors$)$ much easier but increases running time. But

you can be smart and easily halve the running time.

The first subroutine is called integer$\_$div and does integer division with remainder, i$.$e$.,$ given

the operation y$/$x where both y and x are integers, it finds the integer quotient q and the

remainder $0<=$ r $<$ x such that

y $=$ q$*$x $+$ r

The integer$\_$div subroutine will follow this contract:

The second subroutine is called factorize and will find the two factors of a $16-$bit semiprime.

$($Recall$,$ a semiprime is a number that is the product of exactly two prime factors$).$ The contract

for this subroutine is as follows: