Reverse factorial

Question

Well, we all know that if N is given it\'s easy to calculate N!. But what about the inverse?

N! is given and you are about to find N - Is that possible ? I\'m curio

Answer 1

Here is some clojure code:

(defn- reverse-fact-help [n div]
    (cond (not (= 0 (rem n div))) nil
          (= 1 (quot n div)) div
          :else (reverse-fact-help (/ n div) (+ div 1))))
(defn reverse-fact [n] (reverse-fact-help n 2))

Suppose n=120, div=2. 120/2=60, 60/3=20, 20/4=5, 5/5=1, return 5

Suppose n=12, div=2. 12/2=6, 6/3=2, 2/4=.5, return 'nil'