Calculator
Example Data Table
| Input Numbers | GCD | Common Divisors | Count |
|---|---|---|---|
| 12, 18, 24 | 6 | 1, 2, 3, 6 | 4 |
| 20, 30, 50 | 10 | 1, 2, 5, 10 | 4 |
| 16, 24, 40 | 8 | 1, 2, 4, 8 | 4 |
| 21, 49, 63 | 7 | 1, 7 | 2 |
Formula Used
Common divisors of several integers are exactly the positive divisors of their greatest common divisor.
First, compute the greatest common divisor:
G = gcd(n₁, n₂, n₃, ..., nₖ)
Then list every positive divisor d such that
G mod d = 0.
The Euclidean algorithm is used repeatedly:
gcd(a, b) = gcd(b, a mod b),
until the remainder becomes zero.
How to Use This Calculator
- Enter at least two whole numbers in the input box.
- Select a separator mode, or leave it on auto detect.
- Choose ascending or descending divisor order.
- Choose whether to show prime factorization details.
- Press Find Common Divisors.
- Review the summary, common divisors, tables, and graph.
- Export the results as CSV or PDF when needed.
FAQs
1. What does this calculator find?
It finds every positive divisor shared by all entered integers. It also calculates the greatest common divisor, divisor counts, pairwise gcd values, and optional prime factorizations for deeper review.
2. Why is the greatest common divisor important?
The greatest common divisor is the largest whole number dividing every input exactly. Once you know it, all common divisors are simply the positive divisors of that gcd.
3. Can I enter negative numbers?
Yes. Negative inputs are accepted, but divisor analysis uses their absolute values. That keeps the shared factor results mathematically consistent and easy to compare.
4. What happens if I include zero?
Zero is allowed in gcd calculations, but divisor listing for zero is not finite. The tool still computes the shared gcd correctly when combined with nonzero integers.
5. How many numbers can I test?
You can test many integers in one run, limited mostly by practical browser and server resources. For typical educational and planning tasks, the calculator handles standard lists comfortably.
6. What is the pairwise gcd matrix for?
It shows the gcd between every pair of entered numbers. This helps you spot clustering, shared structure, and which values contribute most strongly to the overall common divisor pattern.
7. Why do I see only positive common divisors?
Standard divisor tables usually list positive divisors for clarity. Negative divisors exist too, but they mirror the positive results and rarely improve interpretation in practical workflows.
8. When should I export CSV or PDF?
Use CSV for spreadsheet analysis, recordkeeping, and batch comparison. Use PDF when you want a neat report for sharing, printing, class notes, or project documentation.