diff --git a/pint/quantity.py b/pint/quantity.py
index 9fddf2fc6..60ca45df7 100644
--- a/pint/quantity.py
+++ b/pint/quantity.py
@@ -664,6 +664,8 @@ def __int__(self):
     def __float__(self):
         if self.dimensionless:
             return float(self._convert_magnitude_not_inplace(UnitsContainer()))
+        # else: # ( for math.floor !? )
+        #     return float(self._magnitude)
         raise DimensionalityError(self._units, "dimensionless")
 
     def __complex__(self):
@@ -1092,6 +1094,12 @@ def __rtruediv__(self, other):
     __div__ = __truediv__
     __rdiv__ = __rtruediv__
     __idiv__ = __itruediv__
+    
+    def __ceil__(self):
+        return self.__floordiv__(1) + self.__class__(1, self._units)
+
+    def __floor__(self):
+        return self.__floordiv__(1)
 
     def __ifloordiv__(self, other):
         if self._check(other):
@@ -1099,7 +1107,11 @@ def __ifloordiv__(self, other):
         elif self.dimensionless:
             self._magnitude = self.to("")._magnitude // other
         else:
-            raise DimensionalityError(self._units, "dimensionless")
+            if not hasattr(other, "dimensionless"):
+                magnitude = self._magnitude // other
+                return self.__class__(magnitude, self._units)
+            else:
+                raise DimensionalityError(self._units, "dimensionless")
         self._units = UnitsContainer({})
         return self
 
@@ -1110,7 +1122,11 @@ def __floordiv__(self, other):
         elif self.dimensionless:
             magnitude = self.to("")._magnitude // other
         else:
-            raise DimensionalityError(self._units, "dimensionless")
+            if not hasattr(other, "dimensionless"):
+                magnitude = self._magnitude // other
+                return self.__class__(magnitude, self._units)
+            else:
+                raise DimensionalityError(self._units, "dimensionless")
         return self.__class__(magnitude, UnitsContainer({}))
 
     @check_implemented
@@ -1131,9 +1147,11 @@ def __imod__(self, other):
 
     @check_implemented
     def __mod__(self, other):
-        if not self._check(other):
-            other = self.__class__(other, UnitsContainer({}))
-        magnitude = self._magnitude % other.to(self._units)._magnitude
+        if self._check(other):
+            magnitude = self._magnitude % other.to(self._units)._magnitude
+        else:
+            # other = self.__class__(other, UnitsContainer({}))
+            magnitude = self._magnitude % other
         return self.__class__(magnitude, self._units)
 
     @check_implemented
@@ -1149,9 +1167,15 @@ def __rmod__(self, other):
 
     @check_implemented
     def __divmod__(self, other):
-        if not self._check(other):
-            other = self.__class__(other, UnitsContainer({}))
-        q, r = divmod(self._magnitude, other.to(self._units)._magnitude)
+        if self._check(other):
+            q, r = divmod(self._magnitude, other.to(self._units)._magnitude)
+        else:
+            if not hasattr(other, "dimensionless"):
+                q, r = divmod(self._magnitude, other)
+                return (self.__class__(q, self._units), self.__class__(r, self._units))
+            else:
+                other = self.__class__(other, UnitsContainer({}))
+                q, r = divmod(self._magnitude, other.to(self._units)._magnitude)
         return (self.__class__(q, UnitsContainer({})), self.__class__(r, self._units))
 
     @check_implemented
diff --git a/pint/testsuite/test_quantity.py b/pint/testsuite/test_quantity.py
index 9f02eaccb..fd46a00eb 100644
--- a/pint/testsuite/test_quantity.py
+++ b/pint/testsuite/test_quantity.py
@@ -717,23 +717,23 @@ def _test_quantity_floordiv(self, unit, func):
         b = self.Q_("3*second")
         self.assertRaises(DimensionalityError, op.floordiv, a, b)
         self.assertRaises(DimensionalityError, op.floordiv, 3, b)
-        self.assertRaises(DimensionalityError, op.floordiv, a, 3)
         self.assertRaises(DimensionalityError, op.ifloordiv, a, b)
         self.assertRaises(DimensionalityError, op.ifloordiv, 3, b)
-        self.assertRaises(DimensionalityError, op.ifloordiv, a, 3)
         func(op.floordiv, unit * 10.0, "4.2*meter/meter", 2, unit)
         func(op.floordiv, "10*meter", "4.2*inch", 93, unit)
+        func(op.floordiv, unit * 10.0, 3, 3 * unit, unit)
+        func(op.ifloordiv, unit * 10, 3, 3 * unit, unit)
 
     def _test_quantity_mod(self, unit, func):
         a = self.Q_("10*meter")
         b = self.Q_("3*second")
         self.assertRaises(DimensionalityError, op.mod, a, b)
         self.assertRaises(DimensionalityError, op.mod, 3, b)
-        self.assertRaises(DimensionalityError, op.mod, a, 3)
         self.assertRaises(DimensionalityError, op.imod, a, b)
         self.assertRaises(DimensionalityError, op.imod, 3, b)
-        self.assertRaises(DimensionalityError, op.imod, a, 3)
         func(op.mod, unit * 10.0, "4.2*meter/meter", 1.6, unit)
+        func(op.mod, unit * 10.0, 3, 1 * unit, unit)
+        func(op.imod, unit * 10.0, 3, 1 * unit, unit)
 
     def _test_quantity_ifloordiv(self, unit, func):
         func(op.ifloordiv, 10.0, "4.2*meter/meter", 2, unit)
@@ -782,7 +782,7 @@ def _test_quantity_divmod(self):
         b = self.Q_("3*second")
         self.assertRaises(DimensionalityError, divmod, a, b)
         self.assertRaises(DimensionalityError, divmod, 3, b)
-        self.assertRaises(DimensionalityError, divmod, a, 3)
+        self._test_quantity_divmod_one("10*meter", 3)
 
     def _test_numeric(self, unit, ifunc):
         self._test_quantity_add_sub(unit, self._test_not_inplace)