Factorization Calculators
Find LCM, GCF, and all factors of any number — with step-by-step explanations
Choose Your Calculator
Results & Analysis
📖 Step-by-Step Solution
Enter numbers and click Calculate to see the solution.
⚡ What is LCM?
Least Common Multiple — the smallest number that is a multiple of two or more numbers. Used for adding fractions, scheduling events, and solving ratio problems.
🎯 What is GCF?
Greatest Common Factor — the largest number that divides evenly into two or more numbers. Essential for simplifying fractions and factoring expressions.
🔍 Factor Finder
Lists every number that divides evenly into your target number. Also shows prime factorization — breaking down into prime numbers like 2, 3, 5, 7...
📐 How Factorization Works
LCM (Least Common Multiple): The smallest number that all your input numbers divide into evenly. For 12 and 18, multiples of 12 are 12,24,36... and of 18 are 18,36,54... The first match is 36, so LCM = 36.
GCF (Greatest Common Factor): The largest number that divides all inputs without a remainder. For 24 and 36: factors of 24 are 1,2,3,4,6,8,12,24; factors of 36 are 1,2,3,4,6,9,12,18,36. The largest common is 12.
Prime Factorization: Breaking a number into its prime building blocks. Example: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
🎓 Real-World Examples
Bus A arrives every 12 minutes, Bus B every 18 minutes. When do they arrive together? LCM(12,18) = 36 minutes.
You have 24 slices of pepperoni and 36 slices of cheese. What's the largest number of identical pizzas you can make? GCF(24,36) = 12 slices per pizza.
Simplify 48/60: GCF(48,60) = 12, so 48/60 = 4/5.
❓ Frequently Asked Questions
Yes! Click "Add Another Number" to include as many as you need — up to 10 numbers.
Our calculator only accepts positive integers (1 and above). This follows standard math definitions for LCM and GCF.
It helps find LCM, GCF, simplify radicals, encrypt data (RSA encryption), and solve advanced math problems.
Yes, up to 1 million. For very large numbers, calculations may take a second but will still be accurate.
