diff --git a/src/qr.jl b/src/qr.jl
index 5c59ab60..ffe369b6 100644
--- a/src/qr.jl
+++ b/src/qr.jl
@@ -148,7 +148,8 @@ Base.iterate(S::QRCompactWY, ::Val{:done}) = nothing
 #
 function _triuppers_qr(T)
     blocksize, cols = size(T)
-    return Iterators.map(0:div(cols - 1, blocksize)) do i
+    nblocks = iszero(cols) || iszero(blocksize) ? 0 : cld(cols, blocksize)
+    return Iterators.map(range(0, length=nblocks)) do i
         n = min(blocksize, cols - i * blocksize)
         return UpperTriangular(view(T, 1:n, (1:n) .+ i * blocksize))
     end
@@ -158,9 +159,11 @@ function Base.hash(F::QRCompactWY, h::UInt)
     return hash(F.factors, foldr(hash, _triuppers_qr(F.T); init=hash(QRCompactWY, h)))
 end
 function Base.:(==)(A::QRCompactWY, B::QRCompactWY)
+    size(A.T) == size(B.T) || return false
     return A.factors == B.factors && all(splat(==), zip(_triuppers_qr.((A.T, B.T))...))
 end
 function Base.isequal(A::QRCompactWY, B::QRCompactWY)
+    size(A.T) == size(B.T) || return false
     return isequal(A.factors, B.factors) && all(zip(_triuppers_qr.((A.T, B.T))...)) do (a, b)
         isequal(a, b)::Bool
     end
diff --git a/test/qr.jl b/test/qr.jl
index 0ad61a7a..cc397efe 100644
--- a/test/qr.jl
+++ b/test/qr.jl
@@ -517,7 +517,7 @@ end
             # this should have worked before, Q is square, and R is 0 × 0:
             A_zero_cols = rand(F, dimA, 0)
             qr_zero_cols = qr(A_zero_cols)
-            @test size(qr_zero_cols.Q) == (dimA, dimA)
+            @test size(qr_zero_cols.Q) == (dimA, dimA)
             @test size(qr_zero_cols.R) == (0, 0)
             @test qr_zero_cols.Q == LinearAlgebra.I(dimA)
 
@@ -542,4 +542,23 @@ end
     @test rank(qr([1.0 2.0 3.0; 4.0 5.0 6.0 ; 7.0 8.0 9.0], ColumnNorm())) == 2
 end
 
+@testset "QRCompactWY equality/hash" begin
+    @testset "$(size(A))" for A in (zeros(0, 0), zeros(0, 3), zeros(3, 0))
+        F, G = qr(A), qr(A)
+        @test F == G
+        @test isequal(F, G)
+        @test hash(F) == hash(G)
+    end
+
+    @testset "QRCompactWY equality checks T shape" begin
+        # This is a contrived example, but ensures that we don't violate the hash contract
+        F = LinearAlgebra.QRCompactWY(zeros(1, 1), reshape([1.0], 1, 1))
+        G = LinearAlgebra.QRCompactWY(zeros(1, 1), reshape([1.0 99.0], 1, 2))
+
+        @test F != G
+        @test !isequal(F, G)
+        @test hash(F) != hash(G)
+    end
+end
+
 end # module TestQR