Project Euler, Problem #3, Haskell

-- The prime factors of 13195 are 5, 7, 13 and 29. What is the largest
-- prime factor of the number 600851475143?

divisorGenerator :: Integral a => a -> a -> a
divisorGenerator a b = divisibilityCheck a (div a (div a b + 1))

divisibilityCheck :: Integral a => a -> a -> a
divisibilityCheck a b = if mod a b == 0 then primeCheck a b else limitCheck a b

limitCheck :: Integral a => a -> a -> a
limitCheck a b = if b > 1 then divisorGenerator a b else b

primeCheck :: Integral a => a -> a -> a
primeCheck a b = if null [c | c <- [2 .. div b 2], mod b c == 0] then b else limitCheck a b

initializer :: Integral a => a -> a
initializer a = limitCheck a (div a 2)

main :: IO ()
main = print $ initializer 600851475143

-- 6857

-- real 0m1,211s
-- user 0m1,202s
-- sys  0m0,008s