Factor Calculator
Find all factors (divisors) of any integer — the numbers that divide it evenly. Useful for number theory, simplification and learning math.
How to use the Factor Calculator
- Enter your inputs into the Factor Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The factor enumeration
For each k from 1 to √n: if n mod k = 0, both k and n/k are factors
Only need to check up to the square root because factors come in pairs. After √n, all remaining factors are pairs of factors below it.
Worked example
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. We check up to √36 = 6. Factor pairs: (1,36), (2,18), (3,12), (4,9), (6,6). Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Frequently asked questions
How is this different from prime factorization?
Factors include all divisors. Prime factorization breaks the number into its prime building blocks only. 36 has 9 factors; its prime factorization is 2² × 3².
How many factors does a number have?
If n = p₁^a₁ × p₂^a₂ × ... then the number of factors is (a₁+1)(a₂+1)... For 36 = 2²·3²: (2+1)(2+1) = 9 factors.
What's a perfect square in terms of factors?
A perfect square has an odd number of factors (because √n pairs with itself). 36 has 9 factors — odd, confirms it's a perfect square.