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20 def prime(num): 21 # num is actually a string because input() returns strings. We'll convert it to int 22 num = int(num) 23 24 if num < 0: 25 print("Negative integers can not be prime") 26 quit() 27 if num is 1: 28 print("1 is neither prime nor composite") 29 # See how I lazily terminated program otherwise it'd forward "None"(default behaviour of python when function 30 # returns nothing) rather than True or False. Which could mess up the program. 31 # If we hit this if statement above statement is printed then program exits. 32 quit() # Now you don't need to get sys.exit() to exit python has quit to handle the same thing 33 if num in [2, 3]: 34 # if given argument is 2 or 3, it is prime. We used list without defining a variable which is perfectly valid 35 return True 36 if num % 2 == 0: # excluding all even numbers except two. 37 return False 38 else: 39 # Here we are starting counter variable from 3 in range. Second argument excludes numbers above one third 40 # of the given argument. Third argument in range sets steps to take to 2. This makes loop to iterate odds 41 for x in range(3, int(num/3), 2): 42 # Checking if argument is divisible by counter. % is modulus operator which returns remainder of division 43 if num % x == 0: 44 return False 45 # It's okay to have more than one return statement when program hits return statement it exits the function. 46 return True

746 def prime_number_factorisation(n): 747 if n < 2: 748 return [n] 749 i = 2 750 factors = [] 751 while i * i <= n: 752 if n % i: 753 i += 1 754 else: 755 n //= i 756 factors.append(i) 757 if n > 1: 758 factors.append(n) 759 return factors