Count how often I can divide

Question

The following function counts how often I can divide one number by another:

divs n p = if (n `mod` p == 0) then 1 + divs (n `div` p) p else 0

Is there a shorter way to write divs?

Answer 1

My variant would be:

factors :: Integral i => i -> i -> Int
factors f =
    length . takeWhile (== 0) .
    map (`mod` f) . iterate (`div` f)

The iterate/map pattern is very useful for many problems.