Three numbers
GCF of 24, 36, 6012, so all three numbers can be split into equal groups of 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 numbersExact GCFEuclidean stepsCopy 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.
Recent answers
Recent GCF answers will appear here.
Input tips
Enter at least two positive whole numbers separated by commas, spaces, or semicolons.
Large whole numbers stay exact because the calculation uses BigInt integer math.
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.
What people use it for
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.
Quick examples
Two numbers
GCF of 48 and 18012; 48 = 12 x 4 and 180 = 12 x 15
Larger list
GCF of 81, 153, 2259; each number divides evenly by 9 and no larger shared factor fits all three
Need the guide or a nearby tool?
Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.
- How to use the Greatest Common Factor CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
- CalculatorsBrowse related calculators and utilities in the same category.
- Calculator and utility guidesFind more guides that use real tool inputs and example numbers.
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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.
What do the main Greatest Common Factor Calculator inputs mean?
Enter at least two positive whole numbers. Commas, spaces, and semicolons only separate the numbers; the calculator compares the whole numbers themselves to find the largest divisor they all share.
How should I read the Greatest Common Factor Calculator answer?
The headline GCF is the largest whole number that divides every input evenly. For 24, 36, and 60, a GCF of 12 means each number can be split into equal groups of 12 with nothing left over.
What should I double-check before trusting the Greatest Common Factor Calculator?
Check that every entry is a positive whole number and that none of the numbers are missing. Decimals, negative numbers, zero, one-number factor lists, and common-multiple questions belong in a different workflow.
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.