diff --git a/maths/factorial.py b/maths/factorial.py
index ba61447c7564..9082ad241dc3 100644
--- a/maths/factorial.py
+++ b/maths/factorial.py
@@ -5,25 +5,13 @@
 
 def factorial(number: int) -> int:
     """
-    Calculate the factorial of specified number (n!).
 
-    >>> import math
-    >>> all(factorial(i) == math.factorial(i) for i in range(20))
-    True
-    >>> factorial(0.1)
-    Traceback (most recent call last):
-        ...
-    ValueError: factorial() only accepts integral values
-    >>> factorial(-1)
-    Traceback (most recent call last):
-        ...
-    ValueError: factorial() not defined for negative values
-    >>> factorial(1)
-    1
-    >>> factorial(6)
-    720
-    >>> factorial(0)
-    1
+    Calculate the factorial of a non-negative integer.
+
+    :param n: non-negative integer
+    :return: factorial of n
+    :raises ValueError: if n is negative
+
     """
     if number != int(number):
         raise ValueError("factorial() only accepts integral values")
diff --git a/maths/prime_check.py b/maths/prime_check.py
index a757c4108f24..15fb6cdc6b43 100644
--- a/maths/prime_check.py
+++ b/maths/prime_check.py
@@ -7,37 +7,29 @@
 
 
 def is_prime(number: int) -> bool:
-    """Checks to see if a number is a prime in O(sqrt(n)).
-
-    A number is prime if it has exactly two factors: 1 and itself.
-
-    >>> is_prime(0)
-    False
-    >>> is_prime(1)
-    False
-    >>> is_prime(2)
-    True
-    >>> is_prime(3)
-    True
-    >>> is_prime(27)
-    False
-    >>> is_prime(87)
-    False
-    >>> is_prime(563)
-    True
-    >>> is_prime(2999)
-    True
-    >>> is_prime(67483)
-    False
-    >>> is_prime(16.1)
-    Traceback (most recent call last):
-        ...
-    ValueError: is_prime() only accepts positive integers
-    >>> is_prime(-4)
-    Traceback (most recent call last):
-        ...
-    ValueError: is_prime() only accepts positive integers
     """
+    Check whether a given integer is a prime number.
+
+    A prime number has exactly two distinct positive divisors: 1 and itself.
+
+    :param number: integer to check
+    :return: True if number is prime, False otherwise
+    :raises ValueError: if input is not a positive integer
+    """
+
+    # precondition
+    if not isinstance(number, int) or number < 0:
+        raise ValueError("is_prime() only accepts positive integers")
+
+    if 1 < number < 4:
+        return True
+    if number < 2 or number % 2 == 0 or number % 3 == 0:
+        return False
+
+    for i in range(5, int(math.sqrt(number)) + 1, 6):
+        if number % i == 0 or number % (i + 2) == 0:
+            return False
+    return True
 
     # precondition
     if not isinstance(number, int) or not number >= 0:
diff --git a/strings/check_anagrams.py b/strings/check_anagrams.py
index d747368b2373..03e2c50c3304 100644
--- a/strings/check_anagrams.py
+++ b/strings/check_anagrams.py
@@ -7,8 +7,15 @@
 
 def check_anagrams(first_str: str, second_str: str) -> bool:
     """
-    Two strings are anagrams if they are made up of the same letters but are
-    arranged differently (ignoring the case).
+    Check whether two strings are anagrams of each other.
+
+    Two strings are anagrams if they contain the same characters
+    with the same frequency, ignoring case and whitespace.
+
+    :param first_str: first input string
+    :param second_str: second input string
+    :return: True if strings are anagrams, False otherwise
+
     >>> check_anagrams('Silent', 'Listen')
     True
     >>> check_anagrams('This is a string', 'Is this a string')
diff --git a/strings/palindrome.py b/strings/palindrome.py
index e765207e5942..f4e88c516733 100644
--- a/strings/palindrome.py
+++ b/strings/palindrome.py
@@ -20,10 +20,10 @@
 
 def is_palindrome(s: str) -> bool:
     """
-    Return True if s is a palindrome otherwise return False.
+    Check whether a given string is a palindrome.
 
-    >>> all(is_palindrome(key) is value for key, value in test_data.items())
-    True
+    :param s: input string
+    :return: True if palindrome, False otherwise
     """
 
     start_i = 0