diff --git a/telethon/crypto/factorization.py b/telethon/crypto/factorization.py
index f64b1bd0..359887d3 100644
--- a/telethon/crypto/factorization.py
+++ b/telethon/crypto/factorization.py
@@ -2,17 +2,10 @@ from random import randint
 
 
 class Factorization:
-    @staticmethod
-    def gcd(a: int, b: int) -> int:
-        while b:
-            a, b = b, a % b
-
-        return a
-
     @classmethod
-    def factorize(cls, pq: int) -> tuple or int:
+    def factorize(cls, pq):
         if pq % 2 == 0:
-            return 2
+            return 2, pq // 2
 
         y, c, m = randint(1, pq - 1), randint(1, pq - 1), randint(1, pq - 1)
         g = r = q = 1
@@ -20,15 +13,12 @@ class Factorization:
 
         while g == 1:
             x = y
-
             for i in range(r):
                 y = (pow(y, 2, pq) + c) % pq
 
             k = 0
-
             while k < r and g == 1:
                 ys = y
-
                 for i in range(min(m, r - k)):
                     y = (pow(y, 2, pq) + c) % pq
                     q = q * (abs(x - y)) % pq
@@ -42,8 +32,14 @@ class Factorization:
             while True:
                 ys = (pow(ys, 2, pq) + c) % pq
                 g = cls.gcd(abs(x - ys), pq)
-
                 if g > 1:
                     break
 
         return g, pq // g
+
+    @staticmethod
+    def gcd(a, b):
+        while b:
+            a, b = b, a % b
+
+        return a