haskell problems 001 -> 006

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diff --git a/haskell/003-largest_prime_factor.hs b/haskell/003-largest_prime_factor.hs
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+-- Largest prime factor
+
+-- Problem 3
+-- The prime factors of 13195 are 5, 7, 13 and 29.
+
+-- What is the largest prime factor of the number 600851475143 ?
+
+
+main = do
+    print (last $ factors 600851475143)
+
+factors x = trial_division 2 x
+
+trial_division :: Int -> Int -> [Int]
+trial_division by x
+    | x <= 1 = []
+    | x `mod` by == 0 = by:trial_division by (x `div` by)
+    | otherwise = trial_division (by + 1) x
+