Count Div

Haskell Count Div

countDiv :: Int -> Int -> Int -> Int
countDiv a b k = (lastDiv - firstDiv) `div` k + 1
  where
    firstDiv = if a `mod` k == 0 then a else a + (k - a `mod` k)
    lastDiv  = b - b `mod` k

This counts how many numbers in a range are divisible by K without looping through every value.