Calculator
Enter whole numbers only. Separate values with commas, spaces, semicolons, or new lines.
Example Data Table
| Example Inputs | GCF | Reason |
|---|---|---|
| 48, 72, 120 | 24 | 24 divides all three numbers evenly. |
| 18, 24, 30 | 6 | 6 is the largest shared positive divisor. |
| 0, 45, 60 | 15 | Zero does not reduce the common divisor here. |
| -32, 48, 80 | 16 | Negative signs are ignored for GCF size. |
Formula Used
The calculator mainly uses the Euclidean algorithm. For two integers a and b, the rule is gcd(a, b) = gcd(b, a mod b). The process repeats until the remainder becomes zero. The last nonzero remainder is the greatest common factor.
For more than two integers, the calculator applies the rule pair by pair:
gcd(a, b, c, ... ) = gcd(gcd(a, b), c, ... )
When prime factorization is selected, the calculator also checks the primes shared by every nonzero input and keeps the smallest exponent for each shared prime.
How to Use This Calculator
- Enter at least two whole numbers in the integer field.
- Separate values with commas, spaces, semicolons, or line breaks.
- Choose an algorithm and the display options you want.
- Click Calculate GCF to generate the result summary.
- Review the GCF, factorization, common factors, tables, and Plotly graph.
- Use the CSV or PDF buttons to save your result.
FAQs
1. What is the greatest common factor?
The greatest common factor is the largest positive integer that divides every number in the set without leaving a remainder.
2. Can I enter more than two numbers?
Yes. The calculator accepts multiple integers and reduces them step by step until one final common factor remains.
3. Does the calculator accept negative numbers?
Yes. Negative signs do not change the factor size. The calculator uses absolute values when determining the greatest common factor.
4. What happens when one input is zero?
If one value is zero, the GCF comes from the remaining nonzero values. If all values are zero, the calculator reports a special zero case.
5. Which algorithm should I choose?
Euclidean mode is excellent for fast integer work. Prime factorization helps when you want to inspect shared primes. Hybrid balances speed and detail.
6. Why are only whole numbers allowed?
GCF is usually defined for integers. Decimals and fractions use different simplification methods, so this tool keeps the result mathematically clear.
7. What does the common factors list show?
It lists every positive divisor shared by the full set. The largest item in that list is always the greatest common factor.
8. Why should I download CSV or PDF results?
Downloads help with homework records, tutoring notes, worksheets, and quick result sharing when you need a saved copy.