diff --git a/base/reinterpretarray.jl b/base/reinterpretarray.jl
index 074973496db2bd..276158a78e64ec 100644
--- a/base/reinterpretarray.jl
+++ b/base/reinterpretarray.jl
@@ -155,9 +155,9 @@ function strides(a::ReshapedReinterpretArray)
     els, elp = elsize(a), elsize(ap)
     stp = strides(ap)
     els == elp && return stp
-    els < elp && return (1, map(Fix2(*, elp ÷ els), stp)...)
+    els < elp && return (1, _checked_strides(stp, els, elp)...)
     stp[1] == 1 || throw(ArgumentError("Parent must be contiguous in the 1st dimension!"))
-    return _checked_strides(stp, els ÷ elp)
+    return _checked_strides(tail(stp), els, elp)
 end
 
 function strides(a::NonReshapedReinterpretArray)
@@ -166,12 +166,11 @@ function strides(a::NonReshapedReinterpretArray)
     stp = strides(ap)
     els == elp && return stp
     stp[1] == 1 || throw(ArgumentError("Parent must be contiguous in the 1st dimension!"))
-    els < elp && return (1, map(Fix2(*, elp ÷ els), tail(stp))...)
-    return (1, _checked_strides(stp, els ÷ elp)...)
+    return (1, _checked_strides(tail(stp), els, elp)...)
 end
 
-function _checked_strides(stp, N)
-    drs = map(Fix2(divrem, N), tail(stp))
+@inline function _checked_strides(stp::Tuple, els::Integer, elp::Integer)
+    drs = map(i -> divrem(elp * i, els), stp)
     all(i->iszero(i[2]), drs) || throw(ArgumentError("Parent's strides could not be exactly divided!"))
     map(first, drs)
 end
diff --git a/test/reinterpretarray.jl b/test/reinterpretarray.jl
index de246fd3c5844c..e623b407f70a69 100644
--- a/test/reinterpretarray.jl
+++ b/test/reinterpretarray.jl
@@ -169,8 +169,8 @@ function check_strides(A::AbstractArray)
 end
 
 @testset "strides for NonReshapedReinterpretArray" begin
-    A = Array{Int32}(reshape(1:72, 9, 8))
-    for viewax2 in (1:8, 1:2:6, 7:-1:1, 5:-2:1)
+    A = Array{Int32}(reshape(1:88, 11, 8))
+    for viewax2 in (1:8, 1:2:6, 7:-1:1, 5:-2:1, 2:3:8, 7:-6:1, 3:5:11)
         # dim1 is contiguous
         for T in (Int16, Float32)
             @test check_strides(reinterpret(T, view(A, 1:8, viewax2)))
@@ -180,6 +180,17 @@ end
         else
             @test_throws "Parent's strides" strides(reinterpret(Int64, view(A, 1:8, viewax2)))
         end
+        # non-integer-multipled classified
+        if mod(step(viewax2), 3) == 0
+            @test check_strides(reinterpret(NTuple{3,Int16}, view(A, 2:7, viewax2)))
+        else
+            @test_throws "Parent's strides" strides(reinterpret(NTuple{3,Int16}, view(A, 2:7, viewax2)))
+        end
+        if mod(step(viewax2), 5) == 0
+            @test check_strides(reinterpret(NTuple{5,Int16}, view(A, 2:11, viewax2)))
+        else
+            @test_throws "Parent's strides" strides(reinterpret(NTuple{5,Int16}, view(A, 2:11, viewax2)))
+        end
         # dim1 is not contiguous
         for T in (Int16, Int64)
             @test_throws "Parent must" strides(reinterpret(T, view(A, 8:-1:1, viewax2)))