Math guides that actually make it click
32 in-depth, example-led articles on the Least Common Multiple, Greatest Common Divisor, prime numbers, factors and fractions — written for students, teachers and the curious.
All articles
How to Find the Greatest Common Factor (GCF): 3 Easy Methods (2026)
Find the GCF/GCD/HCF using listing, prime factorization or the Euclidean algorithm, with worked examples…
Where the Greatest Common Factor (GCF) Is Used in Real Life
From simplifying fractions to equal grouping, tiling and recipes — practical GCF applications…
The Factor Tree Method: Prime Factorize Any Number (2026)
Break any number into primes with a factor tree, then write it in exponent form…
Prime Factorization in Exponent (Canonical) Form Explained
Write prime factorizations with exponents and use them for divisors, GCF and LCM…
How Many Factors Does a Number Have? (Divisor Count Formula)
Count factors without listing them using the (exponent + 1) product formula…
Common Factors of Two Numbers Explained (With Examples)
Find every factor two numbers share and how the GCF ties them together…
Prime or Composite? How to Tell the Difference Fast (2026)
Classify any number with the square-root test and divisibility shortcuts…
List of Prime Numbers 1 to 100 (and How to Use the Chart)
The 25 primes under 100, how the sieve builds the chart, and patterns to notice…
Convert Improper Fractions to Mixed Numbers (Step by Step)
Divide to get the whole part and remainder, convert back, and simplify…
Equivalent Fractions Explained (Simplify with the GCF)
Make, simplify and compare equal fractions using the GCF and cross-multiplication…
Find the GCF Using Prime Factorization (GCF & LCM, 2026)
Find the greatest common factor with prime factorization — take the lowest power of each shared prime — and get the LCM too…
How to Check if a Number Is Prime (Fast Methods, 2026)
Check whether a number is prime or composite using the square-root rule and divisibility shortcuts, with worked examples…
Least Common Denominator (LCD): How to Find It — Even With Variables (2026)
The LCD is the LCM of the denominators. Find it for numbers and for algebraic fractions with variables…
Factor Pairs Explained: Find Every Divisor of a Number (2026)
List every divisor of a number by pairing factors up to the square root — and learn what the factor count reveals…
How to Find the LCM: 4 Methods Explained (2026 Guide)
Learn how to find the Least Common Multiple (LCM) using four methods — prime factorization, the GCF formula, listing mul…
LCM vs GCF: What's the Difference? (With Examples)
LCM and GCF are easy to confuse. Learn the difference between the Least Common Multiple and the Greatest Common Factor, …
How to Find the GCD Using the Euclidean Algorithm
The Euclidean algorithm finds the Greatest Common Divisor in just a few steps. Learn how it works, why it works, and how…
Prime Factorization Explained: From Factor Trees to Cryptography
What is prime factorization, how do you do it with a factor tree, and why does it matter? A complete, beginner-friendly …
What Are Prime Numbers? A Complete Beginner's Guide
A clear beginner's guide to prime numbers: the definition, why 1 isn't prime, how to test for primes, famous primes, and…
How to Simplify Fractions Fast (Using the GCD)
Simplify any fraction to lowest terms in one step using the Greatest Common Divisor. Learn the method, see worked exampl…
Finding the Lowest Common Denominator (LCD) for Adding Fractions
The lowest common denominator is just the LCM of the denominators. Learn how to find the LCD and use it to add and compa…
Factors vs Multiples: A Clear Explanation
Factors and multiples are opposites. Learn the difference with simple examples, a memory trick, and how factors and mult…
How to Find All the Factors of a Number
Find every factor of a number efficiently by pairing divisors up to the square root. Learn the method, spot perfect squa…
The Sieve of Eratosthenes: Finding Primes the Smart Way
The Sieve of Eratosthenes finds all primes up to a limit by crossing out multiples. Learn how the ancient algorithm work…
Coprime Numbers Explained (Relatively Prime)
Two numbers are coprime when their GCD is 1. Learn what relatively prime means, how to check it, and why coprimality mat…
Real-World Uses of the LCM (Scheduling, Gears & More)
The LCM isn't just homework. See how the Least Common Multiple solves scheduling, gear timing, packaging and event-align…
Divisibility Rules: Quick Tricks for 2 to 11
Master fast divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10 and 11. These mental shortcuts speed up factoring, simplifyin…
Mental Math: Spotting Prime Numbers Quickly
Learn to recognise prime numbers in your head using a few fast checks. A practical mental-math routine that rules out co…
From Fractions to Ratios: Simplifying in Real Life
Ratios and fractions simplify the same way — by dividing through the GCD. See how this applies to recipes, maps, gear ra…
The Fundamental Theorem of Arithmetic (Why Prime Factorization Is Unique)
The Fundamental Theorem of Arithmetic says every integer above 1 has a unique prime factorization. Learn what it means, …
Teaching LCM & GCD: Tips, Mistakes & Practice Problems
A teacher's guide to LCM and GCD: the best methods to teach, common student mistakes, and ready-to-use practice problems…
How LCM and GCD Power Everyday Programming
From reducing fractions to scheduling tasks and animation loops, LCM and GCD appear all over code. See practical program…