How it works
The Euclidean algorithm iteratively replaces the larger number with the remainder of division, which is fast even for big values. Prime factorization is an alternative when exponents are shown for teaching.
Formula
GCF(a,b) via Euclidean algorithm: repeat GCF(b, a mod b) until b = 0
How to use GCF Calculator
- Enter the integers you want to factor together.
- Calculate to get the GCF.
- Use the result to reduce fractions (divide numerator and denominator by GCF).
- Open the LCM tool if you need a common multiple next.
Worked examples
Concrete numbers and cases you can check against the tool above.
Simplify 84/126
GCF(84, 126) = 42 → divide to get 2/3 in lowest terms.
When to use GCF Calculator
Factoring by trial division wastes time on homework and when simplifying fractions. Pair this with the LCM calculator when both concepts appear in the same problem set.
Common use cases
- Reduce 48/64 to lowest terms.
- Find shared tile size for a rectangular floor layout.
- Complete Euclidean algorithm exercises with a check.
Inputs and outputs
- Positive and negative integers (GCF uses absolute values)
- Multiple numbers
Privacy
This tool runs entirely in your browser. Your data never leaves your device — nothing is uploaded to our servers.
Frequently asked questions
- Is GCF the same as GCD?
- Yes — greatest common factor and greatest common divisor name the same quantity for integers.
- What if the GCF is 1?
- The numbers are coprime (relatively prime): no common factor besides 1.
- How does GCF relate to LCM?
- For two nonzero integers, GCF × LCM = |a × b|. Use that to cross-check results.