diff --git a/Project.toml b/Project.toml
index 5bcc0f4cb..343588085 100644
--- a/Project.toml
+++ b/Project.toml
@@ -21,7 +21,6 @@ MKL_jll = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
-RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
 SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
@@ -45,6 +44,7 @@ KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
 Metal = "dde4c033-4e86-420c-a63e-0dd931031962"
 Pardiso = "46dd5b70-b6fb-5a00-ae2d-e8fea33afaf2"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
 
 [extensions]
 LinearSolveBandedMatricesExt = "BandedMatrices"
@@ -60,6 +60,7 @@ LinearSolveKrylovKitExt = "KrylovKit"
 LinearSolveMetalExt = "Metal"
 LinearSolvePardisoExt = "Pardiso"
 LinearSolveRecursiveArrayToolsExt = "RecursiveArrayTools"
+LinearSolveRecursiveFactorizationExt = "RecursiveFactorization"
 
 [compat]
 AllocCheck = "0.2"
@@ -140,6 +141,7 @@ MultiFloats = "bdf0d083-296b-4888-a5b6-7498122e68a5"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
@@ -147,4 +149,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "Test", "IterativeSolvers", "InteractiveUtils", "JET", "KrylovKit", "KrylovPreconditioners", "Pkg", "Random", "SafeTestsets", "MultiFloats", "ForwardDiff", "HYPRE", "MPI", "BlockDiagonals", "Enzyme", "FiniteDiff", "BandedMatrices", "FastAlmostBandedMatrices", "StaticArrays", "AllocCheck", "StableRNGs", "Zygote"]
+test = ["Aqua", "Test", "IterativeSolvers", "InteractiveUtils", "JET", "KrylovKit", "KrylovPreconditioners", "Pkg", "Random", "SafeTestsets", "MultiFloats", "ForwardDiff", "HYPRE", "MPI", "BlockDiagonals", "Enzyme", "FiniteDiff", "BandedMatrices", "FastAlmostBandedMatrices", "StaticArrays", "AllocCheck", "StableRNGs", "Zygote", "RecursiveFactorization"]
diff --git a/ext/LinearSolveRecursiveFactorizationExt.jl b/ext/LinearSolveRecursiveFactorizationExt.jl
new file mode 100644
index 000000000..c4794c44a
--- /dev/null
+++ b/ext/LinearSolveRecursiveFactorizationExt.jl
@@ -0,0 +1,31 @@
+module LinearSolveRecursiveFactorizationExt
+
+using LinearSolve
+using LinearSolve.LinearAlgebra, LinearSolve.ArrayInterface, RecursiveFactorization
+
+LinearSolve.userecursivefactorization(A::Union{Nothing, AbstractMatrix}) = true
+
+function SciMLBase.solve!(cache::LinearSolve.LinearCache, alg::RFLUFactorization{P, T};
+        kwargs...) where {P, T}
+    A = cache.A
+    A = convert(AbstractMatrix, A)
+    fact, ipiv = LinearSolve.@get_cacheval(cache, :RFLUFactorization)
+    if cache.isfresh
+        if length(ipiv) != min(size(A)...)
+            ipiv = Vector{LinearAlgebra.BlasInt}(undef, min(size(A)...))
+        end
+        fact = RecursiveFactorization.lu!(A, ipiv, Val(P), Val(T), check = false)
+        cache.cacheval = (fact, ipiv)
+
+        if !LinearAlgebra.issuccess(fact)
+            return SciMLBase.build_linear_solution(
+                alg, cache.u, nothing, cache; retcode = ReturnCode.Failure)
+        end
+
+        cache.isfresh = false
+    end
+    y = ldiv!(cache.u, LinearSolve.@get_cacheval(cache, :RFLUFactorization)[1], cache.b)
+    SciMLBase.build_linear_solution(alg, y, nothing, cache)
+end
+
+end
diff --git a/src/LinearSolve.jl b/src/LinearSolve.jl
index 5c83b46aa..485f3c5af 100644
--- a/src/LinearSolve.jl
+++ b/src/LinearSolve.jl
@@ -6,7 +6,6 @@ end
 
 import PrecompileTools
 using ArrayInterface
-using RecursiveFactorization
 using Base: cache_dependencies, Bool
 using LinearAlgebra
 using SparseArrays
@@ -127,6 +126,7 @@ end
 const BLASELTYPES = Union{Float32, Float64, ComplexF32, ComplexF64}
 
 include("common.jl")
+include("extension_algs.jl")
 include("factorization.jl")
 include("appleaccelerate.jl")
 include("mkl.jl")
@@ -137,7 +137,6 @@ include("preconditioners.jl")
 include("solve_function.jl")
 include("default.jl")
 include("init.jl")
-include("extension_algs.jl")
 include("adjoint.jl")
 include("deprecated.jl")
 
@@ -212,7 +211,6 @@ PrecompileTools.@compile_workload begin
     prob = LinearProblem(A, b)
     sol = solve(prob)
     sol = solve(prob, LUFactorization())
-    sol = solve(prob, RFLUFactorization())
     sol = solve(prob, KrylovJL_GMRES())
 end
 
diff --git a/src/default.jl b/src/default.jl
index a0ebb705f..0cb66d06e 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -165,6 +165,8 @@ function defaultalg(A::SciMLBase.AbstractSciMLOperator, b,
     end
 end
 
+userecursivefactorization(A) = false
+
 # Allows A === nothing as a stand-in for dense matrix
 function defaultalg(A, b, assump::OperatorAssumptions{Bool})
     alg = if assump.issq
@@ -178,14 +180,15 @@ function defaultalg(A, b, assump::OperatorAssumptions{Bool})
                (__conditioning(assump) === OperatorCondition.IllConditioned ||
                 __conditioning(assump) === OperatorCondition.WellConditioned)
                 if length(b) <= 10
-                    DefaultAlgorithmChoice.RFLUFactorization
+                    DefaultAlgorithmChoice.GenericLUFactorization
                 elseif appleaccelerate_isavailable() && b isa Array &&
                        eltype(b) <: Union{Float32, Float64, ComplexF32, ComplexF64}
                     DefaultAlgorithmChoice.AppleAccelerateLUFactorization
                 elseif (length(b) <= 100 || (isopenblas() && length(b) <= 500) ||
                         (usemkl && length(b) <= 200)) &&
                        (A === nothing ? eltype(b) <: Union{Float32, Float64} :
-                        eltype(A) <: Union{Float32, Float64})
+                        eltype(A) <: Union{Float32, Float64}) &&
+                       userecursivefactorization(A)
                     DefaultAlgorithmChoice.RFLUFactorization
                     #elseif A === nothing || A isa Matrix
                     #    alg = FastLUFactorization()
@@ -265,7 +268,7 @@ function algchoice_to_alg(alg::Symbol)
     elseif alg === :GenericLUFactorization
         GenericLUFactorization()
     elseif alg === :RFLUFactorization
-        RFLUFactorization()
+        RFLUFactorization(throwerror = false)
     elseif alg === :BunchKaufmanFactorization
         BunchKaufmanFactorization()
     elseif alg === :CHOLMODFactorization
diff --git a/src/extension_algs.jl b/src/extension_algs.jl
index da444912b..fbd52c6cd 100644
--- a/src/extension_algs.jl
+++ b/src/extension_algs.jl
@@ -82,6 +82,31 @@ struct CudaOffloadFactorization <: LinearSolve.AbstractFactorization
     end
 end
 
+## RFLUFactorization
+
+"""
+`RFLUFactorization()`
+
+A fast pure Julia LU-factorization implementation
+using RecursiveFactorization.jl. This is by far the fastest LU-factorization
+implementation, usually outperforming OpenBLAS and MKL for smaller matrices
+(<500x500), but currently optimized only for Base `Array` with `Float32` or `Float64`.
+Additional optimization for complex matrices is in the works.
+"""
+struct RFLUFactorization{P, T} <: AbstractDenseFactorization
+    function RFLUFactorization(::Val{P}, ::Val{T}; throwerror = true) where {P, T}
+        if !userecursivefactorization(nothing)
+            throwerror &&
+                error("RFLUFactorization requires that RecursiveFactorization.jl is loaded, i.e. `using RecursiveFactorization`")
+        end
+        return new{P, T}()
+    end
+end
+
+function RFLUFactorization(; pivot = Val(true), thread = Val(true), throwerror = true)
+    RFLUFactorization(pivot, thread; throwerror)
+end
+
 """
 ```julia
 MKLPardisoFactorize(; nprocs::Union{Int, Nothing} = nothing,
diff --git a/src/factorization.jl b/src/factorization.jl
index 74631d158..f50a1838e 100644
--- a/src/factorization.jl
+++ b/src/factorization.jl
@@ -29,6 +29,36 @@ function init_cacheval(alg::AbstractFactorization, A, b, u, Pl, Pr, maxiters::In
     do_factorization(alg, convert(AbstractMatrix, A), b, u)
 end
 
+## RFLU Factorization
+
+function LinearSolve.init_cacheval(alg::RFLUFactorization, A, b, u, Pl, Pr, maxiters::Int,
+        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
+    ipiv = Vector{LinearAlgebra.BlasInt}(undef, min(size(A)...))
+    ArrayInterface.lu_instance(convert(AbstractMatrix, A)), ipiv
+end
+
+function LinearSolve.init_cacheval(
+        alg::RFLUFactorization, A::Matrix{Float64}, b, u, Pl, Pr,
+        maxiters::Int,
+        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
+    ipiv = Vector{LinearAlgebra.BlasInt}(undef, 0)
+    PREALLOCATED_LU, ipiv
+end
+
+function LinearSolve.init_cacheval(alg::RFLUFactorization,
+        A::Union{AbstractSparseArray, AbstractSciMLOperator}, b, u, Pl, Pr,
+        maxiters::Int,
+        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
+    nothing, nothing
+end
+
+function LinearSolve.init_cacheval(alg::RFLUFactorization,
+        A::Union{Diagonal, SymTridiagonal, Tridiagonal}, b, u, Pl, Pr,
+        maxiters::Int,
+        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
+    nothing, nothing
+end
+
 ## LU Factorizations
 
 """
@@ -989,75 +1019,6 @@ function SciMLBase.solve!(cache::LinearCache, alg::CHOLMODFactorization; kwargs.
     SciMLBase.build_linear_solution(alg, cache.u, nothing, cache)
 end
 
-## RFLUFactorization
-
-"""
-`RFLUFactorization()`
-
-A fast pure Julia LU-factorization implementation
-using RecursiveFactorization.jl. This is by far the fastest LU-factorization
-implementation, usually outperforming OpenBLAS and MKL for smaller matrices
-(<500x500), but currently optimized only for Base `Array` with `Float32` or `Float64`.
-Additional optimization for complex matrices is in the works.
-"""
-struct RFLUFactorization{P, T} <: AbstractDenseFactorization
-    RFLUFactorization(::Val{P}, ::Val{T}) where {P, T} = new{P, T}()
-end
-
-function RFLUFactorization(; pivot = Val(true), thread = Val(true))
-    RFLUFactorization(pivot, thread)
-end
-
-function init_cacheval(alg::RFLUFactorization, A, b, u, Pl, Pr, maxiters::Int,
-        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
-    ipiv = Vector{LinearAlgebra.BlasInt}(undef, min(size(A)...))
-    ArrayInterface.lu_instance(convert(AbstractMatrix, A)), ipiv
-end
-
-function init_cacheval(alg::RFLUFactorization, A::Matrix{Float64}, b, u, Pl, Pr,
-        maxiters::Int,
-        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
-    ipiv = Vector{LinearAlgebra.BlasInt}(undef, 0)
-    PREALLOCATED_LU, ipiv
-end
-
-function init_cacheval(alg::RFLUFactorization,
-        A::Union{AbstractSparseArray, AbstractSciMLOperator}, b, u, Pl, Pr,
-        maxiters::Int,
-        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
-    nothing, nothing
-end
-
-function init_cacheval(alg::RFLUFactorization,
-        A::Union{Diagonal, SymTridiagonal, Tridiagonal}, b, u, Pl, Pr,
-        maxiters::Int,
-        abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
-    nothing, nothing
-end
-
-function SciMLBase.solve!(cache::LinearCache, alg::RFLUFactorization{P, T};
-        kwargs...) where {P, T}
-    A = cache.A
-    A = convert(AbstractMatrix, A)
-    fact, ipiv = @get_cacheval(cache, :RFLUFactorization)
-    if cache.isfresh
-        if length(ipiv) != min(size(A)...)
-            ipiv = Vector{LinearAlgebra.BlasInt}(undef, min(size(A)...))
-        end
-        fact = RecursiveFactorization.lu!(A, ipiv, Val(P), Val(T), check = false)
-        cache.cacheval = (fact, ipiv)
-
-        if !LinearAlgebra.issuccess(fact)
-            return SciMLBase.build_linear_solution(
-                alg, cache.u, nothing, cache; retcode = ReturnCode.Failure)
-        end
-
-        cache.isfresh = false
-    end
-    y = ldiv!(cache.u, @get_cacheval(cache, :RFLUFactorization)[1], cache.b)
-    SciMLBase.build_linear_solution(alg, y, nothing, cache)
-end
-
 ## NormalCholeskyFactorization
 
 """
diff --git a/test/adjoint.jl b/test/adjoint.jl
index 809feba8a..e1c18ec0b 100644
--- a/test/adjoint.jl
+++ b/test/adjoint.jl
@@ -1,6 +1,6 @@
 using Zygote, ForwardDiff
 using LinearSolve, LinearAlgebra, Test
-using FiniteDiff
+using FiniteDiff, RecursiveFactorization
 using LazyArrays: BroadcastArray
 
 n = 4
diff --git a/test/basictests.jl b/test/basictests.jl
index 64ea0c3d5..497af5463 100644
--- a/test/basictests.jl
+++ b/test/basictests.jl
@@ -1,5 +1,5 @@
 using LinearSolve, LinearAlgebra, SparseArrays, MultiFloats, ForwardDiff
-using SciMLOperators
+using SciMLOperators, RecursiveFactorization
 using IterativeSolvers, KrylovKit, MKL_jll, KrylovPreconditioners
 using Test
 import Random
diff --git a/test/default_algs.jl b/test/default_algs.jl
index e6d69fe52..4b795bffb 100644
--- a/test/default_algs.jl
+++ b/test/default_algs.jl
@@ -1,6 +1,6 @@
-using LinearSolve, LinearAlgebra, SparseArrays, Test, JET
+using LinearSolve, RecursiveFactorization, LinearAlgebra, SparseArrays, Test, JET
 @test LinearSolve.defaultalg(nothing, zeros(3)).alg ===
-      LinearSolve.DefaultAlgorithmChoice.RFLUFactorization
+      LinearSolve.DefaultAlgorithmChoice.GenericLUFactorization
 prob = LinearProblem(rand(3, 3), rand(3))
 solve(prob)
 
diff --git a/test/enzyme.jl b/test/enzyme.jl
index 1650c453b..d523036e5 100644
--- a/test/enzyme.jl
+++ b/test/enzyme.jl
@@ -1,6 +1,6 @@
 using Enzyme, ForwardDiff
 using LinearSolve, LinearAlgebra, Test
-using FiniteDiff
+using FiniteDiff, RecursiveFactorization
 
 n = 4
 A = rand(n, n);
diff --git a/test/retcodes.jl b/test/retcodes.jl
index c75442d34..1e33e8adb 100644
--- a/test/retcodes.jl
+++ b/test/retcodes.jl
@@ -1,4 +1,4 @@
-using LinearSolve
+using LinearSolve, RecursiveFactorization
 
 alglist = (
     LUFactorization,