diff --git a/src/Primes.jl b/src/Primes.jl
index 6971891..6025ae0 100644
--- a/src/Primes.jl
+++ b/src/Primes.jl
@@ -357,7 +357,7 @@ function iterate(f::FactorIterator{T}, state=(f.n, T(3))) where T
     tz = trailing_zeros(n)
     tz>0 && return (T(2), Int(tz)), (n >> tz, p)
     if n <= N_SMALL_FACTORS
-        p = _min_factor(n)
+        p = T(_min_factor(n))
         num_p = 1
         while true
             n = div(n, p)
@@ -369,7 +369,7 @@ function iterate(f::FactorIterator{T}, state=(f.n, T(3))) where T
     elseif p == 3 && isprime(n)
         return (n, 1), (T(1), n)
     end
-    for p in p:2:N_SMALL_FACTORS
+    for p in p:T(2):T(N_SMALL_FACTORS)
         _min_factor(p) == p || continue
         num_p = 0
         while true
diff --git a/test/runtests.jl b/test/runtests.jl
index 27b18b9..cb5dc7c 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -247,11 +247,16 @@ end
 @test all([issorted(collect(factor(rand(Int)))) for x in 1:100])
 
 # test eachfactor iteration
-@test iterate(eachfactor(36)) == ((2, 2), (9, 3))
-@test iterate(eachfactor(7^2*5^3)) == ((5, 3), (49, 5))
-@test iterate(eachfactor(257)) == ((257, 1), (1, 257))
-@test iterate(eachfactor(nextprime(2^16))) == ((65537, 1), (1, 65537))
-                    
+for T in (Int32, Int64, BigInt)
+    @test iterate(eachfactor(T(36))) == ((T(2), 2), T.((9, 3)))
+    @test iterate(eachfactor(T(7^2*5^3))) == ((T(5), 3), T.((49, 5)))
+    @test iterate(eachfactor(T(257))) == ((T(257), 1), T.((1, 257)))
+    @test iterate(eachfactor(T(nextprime(2^16)))) == ((T(65537), 1), T.((1, 65537)))
+    for (p,e) in eachfactor(T(901800900))
+        @test (p,e) isa Tuple{T, Int}
+    end
+end
+
 # Lucas-Lehmer
 @test !ismersenneprime(2047)
 @test ismersenneprime(8191)
@@ -341,7 +346,7 @@ divisors_brute_force(n) = [d for d in one(n):n if iszero(n % d)]
 
     for n in 2:1000
         ds = divisors(T(n))
-        @test ds == divisors(-T(n)) 
+        @test ds == divisors(-T(n))
         @test sort!(ds) == divisors_brute_force(T(n))
     end
 end