diff --git a/mlir/lib/Dialect/StandardOps/IR/Ops.cpp b/mlir/lib/Dialect/StandardOps/IR/Ops.cpp
--- a/mlir/lib/Dialect/StandardOps/IR/Ops.cpp
+++ b/mlir/lib/Dialect/StandardOps/IR/Ops.cpp
@@ -1714,6 +1714,16 @@
     }
     return a.sdiv_ov(b, overflowOrDiv0);
   });
+
+  // Fold out division by one.
+  if (auto rhs = operands[1].dyn_cast_or_null<IntegerAttr>()) {
+    if (rhs.getValue() == 1)
+      return lhs();
+  } else if (auto rhs = operands[1].dyn_cast_or_null<SplatElementsAttr>()) {
+    if (rhs.getSplatValue<IntegerAttr>().getValue() == 1)
+      return lhs();
+  } // Assumes all tensors of all ones are splats.
+
   return overflowOrDiv0 ? Attribute() : result;
 }
 
@@ -2240,6 +2250,16 @@
     }
     return a.udiv(b);
   });
+
+  // Fold out division by one.
+  if (auto rhs = operands[1].dyn_cast_or_null<IntegerAttr>()) {
+    if (rhs.getValue() == 1)
+      return lhs();
+  } else if (auto rhs = operands[1].dyn_cast_or_null<SplatElementsAttr>()) {
+    if (rhs.getSplatValue<IntegerAttr>().getValue() == 1)
+      return lhs();
+  } // Assumes all tensors of all ones are splats.
+
   return div0 ? Attribute() : result;
 }
 
diff --git a/mlir/test/Transforms/canonicalize.mlir b/mlir/test/Transforms/canonicalize.mlir
--- a/mlir/test/Transforms/canonicalize.mlir
+++ b/mlir/test/Transforms/canonicalize.mlir
@@ -920,3 +920,41 @@
 // CHECK-NEXT:   }
 // CHECK-NEXT: }
 // CHECK-NEXT: affine.load
+
+// -----
+
+// CHECK-LABEL: func @divi_signed_by_one
+// CHECK-SAME: %[[ARG:[a-zA-Z0-9]+]]
+func @divi_signed_by_one(%arg0: i32) -> (i32) {
+  %c1 = constant 1 : i32
+  %res = divi_signed %arg0, %c1 : i32
+  // CHECK: return %[[ARG]]
+  return %res : i32
+}
+
+// CHECK-LABEL: func @divi_unsigned_by_one
+// CHECK-SAME: %[[ARG:[a-zA-Z0-9]+]]
+func @divi_unsigned_by_one(%arg0: i32) -> (i32) {
+  %c1 = constant 1 : i32
+  %res = divi_unsigned %arg0, %c1 : i32
+  // CHECK: return %[[ARG]]
+  return %res : i32
+}
+
+// CHECK-LABEL: func @tensor_divi_signed_by_one
+// CHECK-SAME: %[[ARG:[a-zA-Z0-9]+]]
+func @tensor_divi_signed_by_one(%arg0: tensor<4x5xi32>) -> tensor<4x5xi32> {
+  %c1 = constant dense<1> : tensor<4x5xi32>
+  %res = divi_signed %arg0, %c1 : tensor<4x5xi32>
+  // CHECK: return %[[ARG]]
+  return %res : tensor<4x5xi32>
+}
+
+// CHECK-LABEL: func @tensor_divi_unsigned_by_one
+// CHECK-SAME: %[[ARG:[a-zA-Z0-9]+]]
+func @tensor_divi_unsigned_by_one(%arg0: tensor<4x5xi32>) -> tensor<4x5xi32> {
+  %c1 = constant dense<1> : tensor<4x5xi32>
+  %res = divi_unsigned %arg0, %c1 : tensor<4x5xi32>
+  // CHECK: return %[[ARG]]
+  return %res : tensor<4x5xi32>
+}
diff --git a/mlir/test/Transforms/parallel-loop-collapsing.mlir b/mlir/test/Transforms/parallel-loop-collapsing.mlir
--- a/mlir/test/Transforms/parallel-loop-collapsing.mlir
+++ b/mlir/test/Transforms/parallel-loop-collapsing.mlir
@@ -37,11 +37,9 @@
 // CHECK:         [[C2:%.*]] = constant 2 : index
 // CHECK:         loop.parallel ([[NEW_I0:%.*]], [[NEW_I1:%.*]], [[NEW_I2:%.*]]) = ([[C0]], [[C0]], [[C0]]) to ([[C2]], [[C1]], [[C1]]) step ([[C1]], [[C1]], [[C1]]) {
 // CHECK:           [[I0:%.*]] = remi_signed [[NEW_I0]], [[C2]] : index
-// CHECK:           [[I3_COUNT:%.*]] = divi_signed [[NEW_I0]], [[C1]] : index
-// CHECK:           [[I4_COUNT:%.*]] = divi_signed [[NEW_I1]], [[C1]] : index
-// CHECK:           [[VAL_16:%.*]] = muli [[I4_COUNT]], [[C13]] : index
+// CHECK:           [[VAL_16:%.*]] = muli [[NEW_I1]], [[C13]] : index
 // CHECK:           [[I4:%.*]] = addi [[VAL_16]], [[C12]] : index
-// CHECK:           [[VAL_18:%.*]] = muli [[I3_COUNT]], [[C10]] : index
+// CHECK:           [[VAL_18:%.*]] = muli [[NEW_I0]], [[C10]] : index
 // CHECK:           [[I3:%.*]] = addi [[VAL_18]], [[C9]] : index
 // CHECK:           [[VAL_20:%.*]] = muli [[NEW_I2]], [[C7]] : index
 // CHECK:           [[I2:%.*]] = addi [[VAL_20]], [[C6]] : index