Factor Calculator Form
Use any non-zero integer. Add Number B only when you want common factors, GCF, and LCM.
Example Data Table
| Number | Positive Factors | Prime Factorization | Factor Pairs | Divisor Count |
|---|---|---|---|---|
| 28 | 1, 2, 4, 7, 14, 28 | 22 × 7 | (1, 28), (2, 14), (4, 7) | 6 |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 22 × 32 | (1, 36), (2, 18), (3, 12), (4, 9), (6, 6) | 9 |
| 45 | 1, 3, 5, 9, 15, 45 | 32 × 5 | (1, 45), (3, 15), (5, 9) | 6 |
Formula Used
Factor Rule
A number d is a factor of n when n mod d = 0.
Factor Pair Rule
If d divides n, then the paired factor is n ÷ d.
Prime Factorization
Write |n| as a product of prime powers: |n| = p1a1 × p2a2 × ... × pkak.
Number of Positive Factors
If |n| = p1a1 × p2a2 × ... × pkak, then τ(n) = (a1 + 1)(a2 + 1)...(ak + 1).
Sum of Positive Factors
σ(n) = ∏ ((pa+1 - 1) ÷ (p - 1)). The calculator also shows the proper-factor sum: σ(n) - |n|.
Greatest Common Factor and Least Common Multiple
GCF(a, b) comes from the largest shared divisor. LCM(a, b) = |ab| ÷ GCF(a, b).
How to Use This Calculator
- Enter Number A as any non-zero integer.
- Add Number B if you also want common factors, GCF, and LCM.
- Use the divisibility test field to check whether another integer divides Number A exactly.
- Set a display range when you want only selected factors shown in the factor list.
- Choose ascending or descending output and decide whether negative factors should appear.
- Press Calculate Factors to show the result above the form.
- Use the CSV or PDF buttons to save the generated report.
Frequently Asked Questions
1. What does this factor calculator find?
It finds factors, factor pairs, prime factorization, divisor count, factor sums, optional common factors, GCF, LCM, and a divisibility check.
2. Why is zero not allowed?
Zero has infinitely many divisors, so a standard finite factor list cannot be produced. That makes ordinary factor-table output impossible.
3. Are negative numbers supported?
Yes. The main mathematics uses the absolute value for factor counts and prime factorization. You can also display negative factors by checking the negative-factor option.
4. What is the difference between factors and factor pairs?
A factor is a single divisor. A factor pair is two divisors multiplied together to recreate the original number, such as 4 and 9 for 36.
5. What does the prime factorization show?
It rewrites the number as a product of prime powers. This is useful for studying divisibility, divisor counts, simplification, and number patterns.
6. When should I enter Number B?
Enter Number B when you want shared divisors between two integers, along with the greatest common factor and least common multiple.
7. What does the graph represent?
The graph plots each positive factor of Number A against its paired factor. It visually shows how the divisor pairs balance around the square root.
8. Can I export the results?
Yes. After calculation, use the CSV button for spreadsheet-style data or the PDF button for a printable report.