Program for finding all the factors of a number in Scheme.

factors.scm

; Finds all factors of a number in O(sqrt n) time.
(define (factors n)
  (define (@factors n i a)
    (cond ((= (modulo n i) 0) (@factors (quotient n i) i (cons i a)))
          ((>= (* i i) n) (if (= 1 n) a (cons n a)))
          (else (@factors n (+ i 1) a))))
  (@factors n 2 `()))

; Multiples all the elements in a list.
(define (mult l)
  (define (@mult l i)
    (if (null? l) i (@mult (cdr l) (* (car l) i))))
  (@mult l 1))

; Tests all numbers between "start" and "end" (e.g. (test 10 100)).
(define (test start end)
  (if (>= start end) #t
    (let ((f (factors start)))
      (begin
        (display "Factors of ")
        (display start)
        (display ": ")
        (display f)
        (display "\n")
        (if (= (mult f) start)
          (test (+ start 1) end)
          (errorf `test "error on ~s" start))))))