- 01Environment Setup (what you'll need)
- 02Variables and print()
- 03Conditionals (if statements)
- 04Loops (for statements)
- 05Writing Your First Function
- 06Working with Lists
- 07Working with Dictionaries (dict)
- 08Loops (while statements)
- 09Working with Strings
- 10Introducing Classes (Object-Oriented Programming)
- 11Error Handling (try...except)
- 12List Comprehensions
- 13Generators and yield
- 14File Handling Basics
- 15The match Statement (Python's switch)
- 16The Conditional (Ternary) Expression
- 17Inheritance (Extending a Class)
- 18Writing Comments
- 19Logical Operators (and, or, not)
- 20Constants (values you agree not to change)
- 21Splitting and Joining Strings (split, join)
- 22Writing None-Safe Code
- 23Searching a List (in and finding the next match)
- 24Transforming a List with map()
- 25Two-Dimensional Lists (grid-shaped data)
- 26Writing a Custom Exception Class
- 27Default Arguments (initial parameter values)
- 28Working with Sets
- 29Checking Correctness with assert (your first step into testing)
- 30Higher-Order Functions (passing a function as an argument)
- 31Stacks and Queues (basic data structures)
- 32Type Conversion (casting) Basics
- 33Intro to Regular Expressions (pattern matching)
- 34The Binary Search Algorithm
- 35Building a Caesar Cipher (a character-shifting cipher)
- 36Understanding How Bubble Sort Works
- 37Building and Displaying Dates (basic year/month/day operations)
- 38Writing Multiple Test Cases Together
- 39Speeding Up Calculations with Memoization (caching)
- 40Normalizing Strings (strip, unifying case)
- 41Shallow Copy vs. Deep Copy
- 42Enum (Enumerated Types) Basics
- 43Flattening a List
- 44Reversing a String and Checking for Palindromes
- 45Pairing Up Two Lists (the zip operation)
- 46Rounding Numbers (floor, ceil, round)
- 47Multi-Line Strings (triple quotes)
- 48Functions That Return Multiple Values (tuples)
- 49Finding the GCD and LCM (the Euclidean algorithm)
- 50Formatting Numbers (padding digits, decimal places)
- 51Cleanup Logic with try/except/finally
- 52Writing Type-Agnostic Functions
- 53The with Statement (Context Managers) Basics
- 54Generating Random Numbers
- 55Bitwise Operators (AND, OR, XOR, shifts)
- 56Class Variables and @staticmethod Basics
- 57Waiting for a Fixed Amount of Time (time.sleep)
- 58Watch Out for Floating-Point Rounding Errors
- 59Type Hints Basics
- 60FizzBuzz (the classic practice problem)
- 61Checking Whether a Number Is Prime
- 62Set Operations (union, intersection, difference)
- 63Converting Number Bases (binary, hex)
- 64Checking Balanced Parentheses (an application of stacks)
- 65Checking Whether Two Words Are Anagrams
- 66Checking Whether a Year Is a Leap Year
- 67Converting Temperature (Celsius to Fahrenheit)
- 68Prime Factorization
- 69[Applied] Build a Household Budget Tool
Prime Factorization
This lesson covers an algorithm for prime factorization — expressing a number as a product of primes — so you can experience the connection between math and programming. It's written for anyone who searched "Python prime factorization" and landed here.
Prime factorization means expressing a number as a product of prime numbers. You find it by trying divisors starting from 2, and continuing to divide by any divisor that works. This is an important idea spanning both math and computer science, and it's part of what makes cryptographic techniques like RSA encryption secure.
The sample code increases a variable, d, starting from 2, dividing n by it repeatedly as long as it divides evenly. Once it no longer divides evenly, d increases by 1 and the next number is tried — repeating this process until n reaches 1, collecting every prime factor into a list called factors.
A common beginner mistake is understanding the roles of the two nested loops. The inner loop handles "how many times does the same number divide evenly," while the outer loop (the while) handles "advancing to the next number to try." Understanding this two-level structure reveals the overall flow of the algorithm.
Tallying the prime factorization results into a dictionary showing "how many of each factor" produces a more practical output. It's a great topic for experiencing the connection between computer-science fundamentals and programming.
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