- Factors
- 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
- Factor count
- 24
How it works
Square factors meet in the middle
Factors of 36 pair as 1×36, 2×18, 3×12, 4×9 and 6×6. The square-root factor appears only once in the list, which explains why perfect squares have an odd number of positive factors.
Understanding factors and prime factorization
A factor divides an integer without leaving a remainder. The factor list and the prime decomposition describe the same integer in different ways: one lists divisors, while the other expresses a product of prime numbers. Check how signs and special inputs are treated in the mode's notes. Multiplying the prime factors back together is a useful way to verify a decomposition.
Integer factorization: formula and assumptions
Test integer divisors up to √n, then divide repeatedly to obtain prime factors.
The input is limited to one trillion to keep trial division responsive.
Worked example
Using the Integer factorization example:
- Positive integer
- 360
Test integer divisors up to √n, then divide repeatedly to obtain prime factors.
Example result
Factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Factor count: 24
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
What is the difference between factors and prime factors?
Factors divide the number without a remainder. Prime factors are prime numbers whose repeated product reconstructs it.
Why is the input limited to one trillion?
This implementation uses bounded trial division. The limit keeps the calculation responsive rather than implying that larger integers lack factors.
Prepared by Finflo. See our methodology and editorial policy.