A familiar situation
Break a number into prime powers when simplifying fractions or studying divisibility.
How to use this calculator
- Enter positive integer.
- Select Calculate to see the answer and its breakdown.
- Keep a scenario, change an input and compare the results.
Use consistent units and check the assumptions below before applying the result.
How prime factorization is calculated
Repeatedly divide by the smallest candidate prime until it no longer divides the remaining value; continue until the remainder itself is prime. The fundamental theorem of arithmetic guarantees that every integer greater than 1 has one unique prime factorization apart from factor order. 360 factors as 2³ × 3² × 5.
n=∏pᵢ^eᵢ, with each pᵢ prime.360 factors as 2³ × 3² × 5.
Assumptions & useful context
The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.
Frequently asked questions
What is the factorization of 1?
It has no prime factors; 1 is the multiplicative identity, not a prime.
How large an integer can I factor?
Inputs are capped at 100,000,000 to keep trial division responsive.