Factor Calculator
List every positive factor of a whole number and show its prime factorization.
Result
Number of positive factors: 12 factors
Only positive factors are listed; each divides the entered whole number with no remainder.
- Positive factors
- 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Prime factorization
- 2^2 × 3 × 7
- Prime number
- No
https://calcgallery.com/everyday-math/factor-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Factor Calculator
- Enter a positive whole number.
- Read the complete ascending list of positive factors and the factor count.
- Use the prime factorization to see which prime numbers multiply to the original number.
Factors come in pairs
If a whole number divides n exactly, both the divisor and the quotient are
factors. Testing divisors only through √n finds every pair without testing
every integer up to n.
Prime factorization repeatedly divides the number by prime divisors and writes the result as a product. For example:
84 = 2^2 × 3 × 7The definitions follow OpenStax Prealgebra 2e.
With your numbers
- Test positive divisors through √84; each exact divisor supplies a paired factor.
- 84 has 12 positive factors and prime factorization 2^2 × 3 × 7.
Quick reference
Only positive factors are listed; each divides the entered whole number with no remainder.
| Example | Number of positive factors |
|---|---|
| Factors of 84 | 12 |
| Factors of 36 | 9 |
| Prime number 17 | 2 |
| Factors of 100 | 9 |
| Factors of 360 | 24 |
| Factors of 1 | 1 |
Common questions about the Factor Calculator
- What is a factor?
- A factor is a whole number that divides the entered number exactly, leaving no remainder.
- Are negative factors included?
- No. The calculator lists positive factors, which is the standard convention for this type of factor list.
- Is 1 a prime number?
- No. A prime number has exactly two positive factors, 1 and itself; 1 has only one.
- How is this different from the GCF calculator?
- This page lists factors of one number. The GCF calculator finds the largest factor shared by two numbers.