12
Greatest Common Factor Calculator
Use this free greatest common factor calculator to find the GCF of two or more positive whole numbers with exact integer math, examples, copy, history, and step-by-step notes.
Two or more numbers Exact GCF Euclidean steps Copy results
Greatest common factor12
- Numbers checked
- 3
- Smallest input
- 24
- Largest input
- 60
Steps
- Start with 24, 36, 60.
- Use the Euclidean algorithm to find the shared factor between each pair.
- Keep reducing the list until one common factor remains.
- The greatest common factor is 12.
How to use the greatest common factor calculator
- Enter at least two positive whole numbers separated by commas, spaces, or semicolons.
- Press Calculate GCF to find the largest shared divisor.
- Review the exact answer, input range, and Euclidean-algorithm style steps.
- Use examples, recent answers, or copy answer while simplifying fractions or ratios.
Common uses
Simplify fractions by finding the largest shared divisor.
Factor numbers in school math, ratios, and divisibility problems.
Find the largest equal group size that fits multiple quantities.
Check multi-number GCF problems with exact integer results.
Examples
12
9
Frequently asked questions
Quick answers about shared factors, simplifying, Euclidean steps, comparing with LCM, and privacy.
What is the greatest common factor?
The greatest common factor is the largest positive whole number that divides every number in the list without a remainder.
How does the GCF Calculator find the answer?
It uses the Euclidean algorithm to compare pairs of numbers, then carries the shared factor through the rest of the list.
Can I find the GCF of more than two numbers?
Yes. Enter two or more positive whole numbers separated by commas, spaces, or semicolons. The calculator returns one shared GCF.
What is the difference between GCF and LCM?
GCF is the largest shared factor. LCM is the smallest shared multiple. GCF helps with simplifying, while LCM helps with common denominators and repeating schedules.
Can the GCF be 1?
Yes. If the numbers do not share any factor larger than 1, the greatest common factor is 1.
Is my GCF history private?
Yes. Recent GCF answers stay only in the current browser tab while you use the page. They are not sent to a server.
Related tools
Least Common Multiple Calculator Find the least common multiple of two or more whole numbers with steps. Open Factor Calculator List factors, factor pairs, and prime factorization for a whole number. Open Ratio Calculator Simplify ratios, find equivalent ratios, and split totals by ratio parts. Open