Greatest Common Factor Calculator
Calculate Greatest Common Factor (GCF/GCD) and Least Common Multiple (LCM) of two or more numbers. Shows prime factorization step-by-step. Free.
Greatest Common Factor Calculator
toolznova.com • Free Calculator
How to Use
Calculate GCF and LCM in 3 steps.
Enter Numbers
Type 2 or more positive integers separated by commas.
Click Calculate
Click Calculate GCF & LCM for instant results.
See Results
View GCF, LCM, and prime factorization of all numbers.
Why ToolzNova?
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Results in milliseconds.
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Precise formulas every time.
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Everywhere
Mobile, tablet, desktop.
Why Calculate GCF and LCM?
- Fractions: GCF used to simplify fractions to lowest terms.
- Adding Fractions: LCM finds the least common denominator.
- Scheduling: LCM shows when recurring events next coincide.
- Division: GCF helps split items into equal groups exactly.
- Cryptography: GCD is fundamental to RSA encryption algorithm.
- Number Theory: Core concepts for advanced mathematics.
Tips & Examples
- GCF also called GCD (Greatest Common Divisor).
- GCF × LCM = a × b (for exactly two numbers).
- GCF of prime numbers = 1 (coprime — no common factors).
- To simplify fraction: divide numerator and denominator by GCF.
- To add fractions: find LCM of denominators first.
- LCM of consecutive integers n and n+1 is always n×(n+1).
Free GCF and LCM Calculator Online
ToolzNova's free GCF and LCM calculator finds the Greatest Common Factor and Least Common Multiple of two or more numbers simultaneously, with prime factorization of each number shown.
GCF is the largest number that divides all given numbers exactly — used to simplify fractions. LCM is the smallest number divisible by all given numbers — used to add fractions and solve scheduling problems.
GCF and LCM Methods
Euclidean Algorithm: gcd(a,b) = gcd(b, a mod b) until b=0. LCM(a,b) = a×b/GCF(a,b). For multiple numbers: apply iteratively. These algorithms are extremely efficient even for large numbers.