diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
index 56eb3f99b39d2..0d384c61f978e 100644
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -369,9 +369,9 @@ static void computeKnownBitsAddSub(bool Add, const Value *Op0, const Value *Op1,
 }
 
 static void computeKnownBitsMul(const Value *Op0, const Value *Op1, bool NSW,
-                                const APInt &DemandedElts, KnownBits &Known,
-                                KnownBits &Known2, unsigned Depth,
-                                const SimplifyQuery &Q) {
+                                bool NUW, const APInt &DemandedElts,
+                                KnownBits &Known, KnownBits &Known2,
+                                unsigned Depth, const SimplifyQuery &Q) {
   computeKnownBits(Op1, DemandedElts, Known, Depth + 1, Q);
   computeKnownBits(Op0, DemandedElts, Known2, Depth + 1, Q);
 
@@ -390,6 +390,13 @@ static void computeKnownBitsMul(const Value *Op0, const Value *Op1, bool NSW,
       // The product of two numbers with the same sign is non-negative.
       isKnownNonNegative = (isKnownNegativeOp1 && isKnownNegativeOp0) ||
                            (isKnownNonNegativeOp1 && isKnownNonNegativeOp0);
+      if (!isKnownNonNegative && NUW) {
+        // mul nuw nsw with a factor > 1 is non-negative.
+        KnownBits One = KnownBits::makeConstant(APInt(Known.getBitWidth(), 1));
+        isKnownNonNegative = KnownBits::sgt(Known, One).value_or(false) ||
+                             KnownBits::sgt(Known2, One).value_or(false);
+      }
+
       // The product of a negative number and a non-negative number is either
       // negative or zero.
       if (!isKnownNonNegative)
@@ -1090,8 +1097,9 @@ static void computeKnownBitsFromOperator(const Operator *I,
     break;
   case Instruction::Mul: {
     bool NSW = Q.IIQ.hasNoSignedWrap(cast<OverflowingBinaryOperator>(I));
-    computeKnownBitsMul(I->getOperand(0), I->getOperand(1), NSW, DemandedElts,
-                        Known, Known2, Depth, Q);
+    bool NUW = Q.IIQ.hasNoUnsignedWrap(cast<OverflowingBinaryOperator>(I));
+    computeKnownBitsMul(I->getOperand(0), I->getOperand(1), NSW, NUW,
+                        DemandedElts, Known, Known2, Depth, Q);
     break;
   }
   case Instruction::UDiv: {
@@ -1961,7 +1969,7 @@ static void computeKnownBitsFromOperator(const Operator *I,
         case Intrinsic::umul_with_overflow:
         case Intrinsic::smul_with_overflow:
           computeKnownBitsMul(II->getArgOperand(0), II->getArgOperand(1), false,
-                              DemandedElts, Known, Known2, Depth, Q);
+                              false, DemandedElts, Known, Known2, Depth, Q);
           break;
         }
       }
diff --git a/llvm/test/Transforms/InstCombine/ashr-lshr.ll b/llvm/test/Transforms/InstCombine/ashr-lshr.ll
index 49041906680b3..1abf1be2cbedd 100644
--- a/llvm/test/Transforms/InstCombine/ashr-lshr.ll
+++ b/llvm/test/Transforms/InstCombine/ashr-lshr.ll
@@ -741,7 +741,7 @@ define i32 @lshr_mul_times_5_div_4_exact_2(i32 %x) {
 
 define i32 @ashr_mul_times_3_div_2(i32 %0) {
 ; CHECK-LABEL: @ashr_mul_times_3_div_2(
-; CHECK-NEXT:    [[TMP2:%.*]] = ashr i32 [[TMP0:%.*]], 1
+; CHECK-NEXT:    [[TMP2:%.*]] = lshr i32 [[TMP0:%.*]], 1
 ; CHECK-NEXT:    [[ASHR:%.*]] = add nuw nsw i32 [[TMP0]], [[TMP2]]
 ; CHECK-NEXT:    ret i32 [[ASHR]]
 ;
@@ -815,7 +815,7 @@ define i32 @ashr_mul_times_3_div_2_exact_2(i32 %x) {
 
 define i32 @ashr_mul_times_5_div_4(i32 %0) {
 ; CHECK-LABEL: @ashr_mul_times_5_div_4(
-; CHECK-NEXT:    [[TMP2:%.*]] = ashr i32 [[TMP0:%.*]], 2
+; CHECK-NEXT:    [[TMP2:%.*]] = lshr i32 [[TMP0:%.*]], 2
 ; CHECK-NEXT:    [[ASHR:%.*]] = add nuw nsw i32 [[TMP0]], [[TMP2]]
 ; CHECK-NEXT:    ret i32 [[ASHR]]
 ;
diff --git a/llvm/test/Transforms/InstCombine/known-bits.ll b/llvm/test/Transforms/InstCombine/known-bits.ll
index 8cfb987e422f3..aa24ec3905f13 100644
--- a/llvm/test/Transforms/InstCombine/known-bits.ll
+++ b/llvm/test/Transforms/InstCombine/known-bits.ll
@@ -2051,6 +2051,71 @@ exit:
   ret i16 %conv
 }
 
+define i1 @mul_nuw_nsw_nonneg_const(i8 %x) {
+; CHECK-LABEL: @mul_nuw_nsw_nonneg_const(
+; CHECK-NEXT:    ret i1 true
+;
+  %mul = mul nuw nsw i8 %x, 3
+  %cmp = icmp sgt i8 %mul, -1
+  ret i1 %cmp
+}
+
+define i1 @mul_nuw_nsw_nonneg_const_missing_nuw(i8 %x) {
+; CHECK-LABEL: @mul_nuw_nsw_nonneg_const_missing_nuw(
+; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt i8 [[X:%.*]], -1
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %mul = mul nsw i8 %x, 3
+  %cmp = icmp sgt i8 %mul, -1
+  ret i1 %cmp
+}
+
+define i1 @mul_nuw_nsw_nonneg_const_missing_nsw(i8 %x) {
+; CHECK-LABEL: @mul_nuw_nsw_nonneg_const_missing_nsw(
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw i8 [[X:%.*]], 3
+; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt i8 [[MUL]], -1
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %mul = mul nuw i8 %x, 3
+  %cmp = icmp sgt i8 %mul, -1
+  ret i1 %cmp
+}
+
+define i1 @mul_nuw_nsw_nonneg_can_be_one(i8 %x, i8 %y) {
+; CHECK-LABEL: @mul_nuw_nsw_nonneg_can_be_one(
+; CHECK-NEXT:    [[Y_NNEG:%.*]] = and i8 [[Y:%.*]], 127
+; CHECK-NEXT:    [[MUL:%.*]] = mul nuw nsw i8 [[X:%.*]], [[Y_NNEG]]
+; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt i8 [[MUL]], -1
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %y.nneg = and i8 %y, 127
+  %mul = mul nuw nsw i8 %x, %y.nneg
+  %cmp = icmp sgt i8 %mul, -1
+  ret i1 %cmp
+}
+
+define i1 @mul_nuw_nsw_nonneg_cant_be_one(i8 %x, i8 %y) {
+; CHECK-LABEL: @mul_nuw_nsw_nonneg_cant_be_one(
+; CHECK-NEXT:    ret i1 true
+;
+  %y.nneg = and i8 %y, 127
+  %y.nneg.not.one = or i8 %y.nneg, 2
+  %mul = mul nuw nsw i8 %x, %y.nneg.not.one
+  %cmp = icmp sgt i8 %mul, -1
+  ret i1 %cmp
+}
+
+define i1 @mul_nuw_nsw_nonneg_cant_be_one_commuted(i8 %x, i8 %y) {
+; CHECK-LABEL: @mul_nuw_nsw_nonneg_cant_be_one_commuted(
+; CHECK-NEXT:    ret i1 true
+;
+  %y.nneg = and i8 %y, 127
+  %y.nneg.not.one = or i8 %y.nneg, 2
+  %mul = mul nuw nsw i8 %y.nneg.not.one, %x
+  %cmp = icmp sgt i8 %mul, -1
+  ret i1 %cmp
+}
+
 declare void @dummy()
 declare void @use(i1)
 declare void @sink(i8)
diff --git a/llvm/test/Transforms/InstCombine/rem-mul-shl.ll b/llvm/test/Transforms/InstCombine/rem-mul-shl.ll
index 9e2df157c2c85..45db2cf675852 100644
--- a/llvm/test/Transforms/InstCombine/rem-mul-shl.ll
+++ b/llvm/test/Transforms/InstCombine/rem-mul-shl.ll
@@ -8,7 +8,7 @@ define i8 @srem_non_matching(i8 %X, i8 %Y) {
 ; CHECK-LABEL: @srem_non_matching(
 ; CHECK-NEXT:    [[BO0:%.*]] = mul nuw nsw i8 [[X:%.*]], 15
 ; CHECK-NEXT:    [[BO1:%.*]] = mul nuw nsw i8 [[Y:%.*]], 5
-; CHECK-NEXT:    [[R:%.*]] = srem i8 [[BO0]], [[BO1]]
+; CHECK-NEXT:    [[R:%.*]] = urem i8 [[BO0]], [[BO1]]
 ; CHECK-NEXT:    ret i8 [[R]]
 ;
   %BO0 = mul nsw nuw i8 %X, 15