diff --git a/NEWS.md b/NEWS.md
index c619d63364620..12b0d3a5b8c88 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -41,6 +41,7 @@ Standard library changes
 ------------------------
 
 * `islowercase` and `isuppercase` are now compliant with the Unicode lower/uppercase categories ([#38574]).
+* `iseven` and `isodd` functions now support non-`Integer` numeric types ([#38976]).
 
 #### Package Manager
 
diff --git a/base/float.jl b/base/float.jl
index d28bc17601a2b..cb4000b51fac2 100644
--- a/base/float.jl
+++ b/base/float.jl
@@ -763,6 +763,8 @@ function issubnormal(x::T) where {T<:IEEEFloat}
 end
 
 ispow2(x::AbstractFloat) = !iszero(x) && frexp(x)[1] == 0.5
+iseven(x::AbstractFloat) = isinteger(x) && (abs(x) > maxintfloat(x) || iseven(Integer(x)))
+isodd(x::AbstractFloat) = isinteger(x) && abs(x) ≤ maxintfloat(x) && isodd(Integer(x))
 
 @eval begin
     typemin(::Type{Float16}) = $(bitcast(Float16, 0xfc00))
diff --git a/base/int.jl b/base/int.jl
index b3acd29c6492f..02a9ace0fe3f1 100644
--- a/base/int.jl
+++ b/base/int.jl
@@ -93,9 +93,9 @@ inv(x::Integer) = float(one(x)) / float(x)
 (/)(x::BitInteger, y::BitInteger) = float(x) / float(y)
 
 """
-    isodd(x::Integer) -> Bool
+    isodd(x::Number) -> Bool
 
-Return `true` if `x` is odd (that is, not divisible by 2), and `false` otherwise.
+Return `true` if `x` is an odd integer (that is, an integer not divisible by 2), and `false` otherwise.
 
 # Examples
 ```jldoctest
@@ -106,12 +106,13 @@ julia> isodd(10)
 false
 ```
 """
-isodd(n::Integer) = rem(n, 2) != 0
+isodd(n::Number) = isreal(n) && isodd(real(n))
+isodd(n::Real) = isinteger(n) && !iszero(rem(Integer(n), 2))
 
 """
-    iseven(x::Integer) -> Bool
+    iseven(x::Number) -> Bool
 
-Return `true` if `x` is even (that is, divisible by 2), and `false` otherwise.
+Return `true` if `x` is an even integer (that is, an integer divisible by 2), and `false` otherwise.
 
 # Examples
 ```jldoctest
@@ -122,7 +123,8 @@ julia> iseven(10)
 true
 ```
 """
-iseven(n::Integer) = !isodd(n)
+iseven(n::Number) = isreal(n) && iseven(real(n))
+iseven(n::Real) = isinteger(n) && iszero(rem(Integer(n), 2))
 
 signbit(x::Integer) = x < 0
 signbit(x::Unsigned) = false
diff --git a/test/complex.jl b/test/complex.jl
index 27fbcee370460..56c446896bf53 100644
--- a/test/complex.jl
+++ b/test/complex.jl
@@ -1205,9 +1205,12 @@ end
 # complex with non-concrete eltype
 @test_throws ErrorException complex(Union{Complex{Int}, Nothing}[])
 
-@testset "ispow2" begin
+@testset "ispow2 and iseven/isodd" begin
     @test ispow2(4+0im)
     @test ispow2(0.25+0im)
     @test !ispow2(4+5im)
     @test !ispow2(7+0im)
+    @test iseven(6+0im) && !isodd(6+0im)
+    @test !iseven(7+0im) && isodd(7+0im)
+    @test !iseven(6+1im) && !isodd(7+1im)
 end
diff --git a/test/floatfuncs.jl b/test/floatfuncs.jl
index 210b487f0f909..e3f3203e3c069 100644
--- a/test/floatfuncs.jl
+++ b/test/floatfuncs.jl
@@ -40,7 +40,7 @@ end
     end
 end
 
-@testset "ispow2" begin
+@testset "ispow2 and iseven/isodd" begin
     for T in (Float16,Float32,Float64,BigFloat)
         for x in (0.25, 1.0, 4.0, exp2(T(exponent(floatmax(T)))), exp2(T(exponent(floatmin(T)))))
             @test ispow2(T(x))
@@ -48,6 +48,15 @@ end
         for x in (1.5, 0.0, 7.0, NaN, Inf)
             @test !ispow2(T(x))
         end
+        for x in (0, 134)
+            @test iseven(T(x)) && iseven(T(-x))
+            @test isodd(T(x+1)) && isodd(T(-x-1))
+        end
+        let x = maxintfloat(T) * π
+            @test iseven(x) && iseven(-x)
+            @test !isodd(x) && !isodd(-x)
+        end
+        @test !iseven(0.5) && !isodd(0.5)
     end
 end
 
diff --git a/test/rational.jl b/test/rational.jl
index 863ab6e1d27f8..961eb93a94ed9 100644
--- a/test/rational.jl
+++ b/test/rational.jl
@@ -595,11 +595,14 @@ end
     @test -2//3 * 0x1 == 0x1 * -2//3 == -2//3
 end
 
-@testset "ispow2" begin
+@testset "ispow2 and iseven/isodd" begin
     @test ispow2(4//1)
     @test ispow2(1//8)
     @test !ispow2(3//8)
     @test !ispow2(0//1)
+    @test iseven(4//1) && !isodd(4//1)
+    @test !iseven(3//1) && isodd(3//1)
+    @test !iseven(3//8) && !isodd(3//8)
 end
 
 @testset "checked_den with different integer types" begin