diff --git a/test/test_uops.py b/test/test_uops.py
index 65fef7a9a3..dfd6a7f967 100644
--- a/test/test_uops.py
+++ b/test/test_uops.py
@@ -402,6 +402,14 @@ class TestAssembly(unittest.TestCase):
     self.assertIn(Ops.SHR, ops)
     self.assertNotIn(Ops.IDIV, ops)
 
+  def test_fast_idiv_remove_powers_of_two(self):
+    ridx = UOp.range(dtypes.int, 2**20, 0)
+    uops = to_uops_list([ridx//(7*64)], opts=Device[Device.DEFAULT].renderer)
+    ops = [x.op for x in uops]
+    # this requires shifting out the powers of two before doing fast_idiv
+    # (((ridx0>>6)*18725)>>17) instead of (int)((((long)(ridx0)*1198373)>>29))
+    self.assertNotIn(Ops.CAST, ops)
+
   def test_mulacc_unrolled(self):
     # test that     acc = acc + a0*b0 + a1*b1 + a2*b2 + a3*b3
     # is not        acc = acc + (a0*b0 + a1*b1 + a2*b2 + a3*b3)
diff --git a/tinygrad/uop/decompositions.py b/tinygrad/uop/decompositions.py
index 4431ea180c..dd807f905c 100644
--- a/tinygrad/uop/decompositions.py
+++ b/tinygrad/uop/decompositions.py
@@ -280,7 +280,7 @@ def magicgu(vmax:int, d:int) -> tuple[int,int]:
       return m, s
   assert False
 
-def fast_idiv(device: str, x: UOp, d: int) -> UOp|None:
+def fast_idiv(device: str, x: UOp, d: int, dont_cast=False) -> UOp|None:
   # If d is a power of two this is not valid for signed ints!
   is_unsigned = True if x.vmin>=0 or x.dtype in dtypes.uints else False
   assert d>0, "Sign should have been taken out of divisor"
@@ -288,6 +288,10 @@ def fast_idiv(device: str, x: UOp, d: int) -> UOp|None:
   m,s = magicgu(max(vmax, abs(vmin)), d)
   if m*vmin >= dtypes.min(x.dtype) and m*vmax <= dtypes.max(x.dtype):
     return ((x*m) >> s) if is_unsigned else ((x*m) >> s) + (x<0).where(x.ufix(1), 0)
+  # before we try casting to a larger dtype (slow), we see if there are powers of two in d we can shift to make x smaller
+  if (largest_factor_of_two_in_d := (d & -d)) > 1:
+    if (ret:=fast_idiv(device, x//largest_factor_of_two_in_d, d//largest_factor_of_two_in_d, dont_cast=True)) is not None: return ret
+  if dont_cast: return None
   # promo_lattice needs to return an unsigned type if the type is unsigned
   if dtypes.is_int(next_dtype := promo_lattice[x.dtype][-1]) and is_dtype_supported(next_dtype, None if device=='' else device):
     if m*vmin >= dtypes.min(next_dtype) and m*vmax <= dtypes.max(next_dtype):