;; (divides? m n) returns #t if m is a divisor of n, and #f otherwise
;; m should not be 0

(define (divides? m n)
  (= (modulo n m) 0))


;; (lowest-factor n trial) returns the lowest factor of n that is 
;; greater than or equal to trial.
;; trial should be at least 2.
;; (If no there is no factor less than n itself, n will be returned.)
;; Note that this is inefficient, for a number of reasons, but it is clear.

(define (lowest-factor n trial)
  (if (divides? trial n)
      trial
      (lowest-factor n (+ 1 trial))))


;; (factors n) returns the list of prime factors of n.
;; n should be positive.
;; Method: find the lowest factor of n, divide it out, then recurse.
;; cons is used to construct the list recursively, outside-in, 
;; starting with the lowest factor

(define (factors n)
  (if (= n 1)
      (list)
      (let (
            (LF (lowest-factor n 2))
            )
        (cons LF (factors (/ n LF))))))