write a function get factors()$()$ that takes a number x and returns a list object. The list  

object should contain a vector of unique prime factors of x and the corresponding exponents.

Additionally, write one helper function is prime()$()$ that returns a logical vector depending on

whether or not the elements in x are prime. A good way to test this function should be:

x <−$<-$ sample($($x =1$=1$e4,$4,$ size =1)$=1)$

y <−$<-$ get_$\_$factors($($x)$)$

this_$\_$works <−$<-$ prod($($y$primes^$^$y$exponents)==$)==$ x & all($($is_$\_$prime($($y$primes))$))$

It is a necessary, but not sufficient, condition that this works ==$==$ TRUE for your function to work

as intended. ($($It will largely depend on if your is prime()$()$ function is correct.)$)$