diff --git a/Data/Monoid/Factorial.hs b/Data/Monoid/Factorial.hs
--- a/Data/Monoid/Factorial.hs
+++ b/Data/Monoid/Factorial.hs
@@ -197,8 +197,50 @@
 
 instance (FactorialMonoid a, FactorialMonoid b) => FactorialMonoid (a, b) where
    factors (a, b) = List.map (\a-> (a, mempty)) (factors a) ++ List.map ((,) mempty) (factors b)
+   primePrefix (a, b) | null a = (a, primePrefix b)
+                      | otherwise = (primePrefix a, mempty)
+   primeSuffix (a, b) | null b = (primeSuffix a, b)
+                      | otherwise = (mempty, primeSuffix b)
+   splitPrimePrefix (a, b) = case (splitPrimePrefix a, splitPrimePrefix b)
+                             of (Just (ap, as), _) -> Just ((ap, mempty), (as, b))
+                                (Nothing, Just (bp, bs)) -> Just ((a, bp), (a, bs))
+                                (Nothing, Nothing) -> Nothing
+   splitPrimeSuffix (a, b) = case (splitPrimeSuffix a, splitPrimeSuffix b)
+                             of (_, Just (bp, bs)) -> Just ((a, bp), (mempty, bs))
+                                (Just (ap, as), Nothing) -> Just ((ap, b), (as, b))
+                                (Nothing, Nothing) -> Nothing
+   foldl f a (x, y) = foldl f2 (foldl f1 a x) y
+      where f1 a = f a . fromFst
+            f2 a = f a . fromSnd
+   foldl' f a (x, y) = a' `seq` foldl f2 a' y
+      where f1 a = f a . fromFst
+            f2 a = f a . fromSnd
+            a' = foldl f1 a x
+   foldr f a (x, y) = foldr (f . fromFst) (foldr (f . fromSnd) a y) x
+   foldMap f (x, y) = foldMap (f . fromFst) x `mappend` foldMap (f . fromSnd) y
    length (a, b) = length a + length b
+   span p (x, y) = ((xp, yp), (xs, ys))
+      where (xp, xs) = span (p . fromFst) x
+            (yp, ys) | null xs = span (p . fromSnd) y
+                     | otherwise = (mempty, y)
+   split p (x, y) = fst $ List.foldr combine (ys, False) xs
+      where xs = List.map fromFst $ split (p . fromFst) x
+            ys = List.map fromSnd $ split (p . fromSnd) y
+            combine x (y:ys, False) = (mappend x y : ys, True)
+            combine x (xs, True) = (x:xs, True)
+   splitAt n (x, y) = ((xp, yp), (xs, ys))
+      where (xp, xs) = splitAt n x
+            (yp, ys) | null xs = splitAt (n - length x) y
+                     | otherwise = (mempty, y)
    reverse (a, b) = (reverse a, reverse b)
+
+{-# INLINE fromFst #-}
+fromFst :: Monoid b => a -> (a, b)
+fromFst a = (a, mempty)
+
+{-# INLINE fromSnd #-}
+fromSnd :: Monoid a => b -> (a, b)
+fromSnd b = (mempty, b)
 
 instance FactorialMonoid [x] where
    factors xs = List.map (:[]) xs
diff --git a/monoid-subclasses.cabal b/monoid-subclasses.cabal
--- a/monoid-subclasses.cabal
+++ b/monoid-subclasses.cabal
@@ -1,5 +1,5 @@
 Name:                monoid-subclasses
-Version:             0.3.4
+Version:             0.3.4.1
 Cabal-Version:       >= 1.10
 Build-Type:          Simple
 Synopsis:            Subclasses of Monoid
@@ -23,8 +23,8 @@
 Library
   Exposed-Modules:   Data.Monoid.Cancellative, Data.Monoid.Factorial, Data.Monoid.Null, Data.Monoid.Textual,
                      Data.Monoid.Instances.ByteString.UTF8, Data.Monoid.Instances.Concat, Data.Monoid.Instances.Measured
-  Build-Depends:     base < 5, bytestring >= 0.9 && < 1.0, containers == 0.5.*, text == 0.11.*, primes == 0.2.*,
-                     vector >= 0.9 && < 0.11
+  Build-Depends:     base < 5, bytestring >= 0.9 && < 1.0, containers == 0.5.*, text >= 0.11 && < 1.1,
+                     primes == 0.2.*, vector >= 0.9 && < 0.11
   GHC-prof-options:  -auto-all
   if impl(ghc >= 7.0.0)
      default-language: Haskell2010
@@ -32,8 +32,8 @@
 test-suite Main
   Type:              exitcode-stdio-1.0
   x-uses-tf:         true
-  Build-Depends:     base < 5, bytestring >= 0.9 && < 1.0, containers == 0.5.*, text == 0.11.*, primes == 0.2.*,
-                     vector >= 0.9 && < 0.11, QuickCheck == 2.*, quickcheck-instances == 0.3.*,
+  Build-Depends:     base < 5, bytestring >= 0.9 && < 1.0, containers == 0.5.*, text >= 0.11 && < 1.1,
+                     primes == 0.2.*, vector >= 0.9 && < 0.11, QuickCheck == 2.*, quickcheck-instances == 0.3.*,
                      test-framework >= 0.4.1, test-framework-quickcheck2
   Main-is:           Test/TestMonoidSubclasses.hs
   Other-Modules:     Data.Monoid.Cancellative, Data.Monoid.Factorial, Data.Monoid.Null, Data.Monoid.Textual,