Factors & Prime Factorization Calculator
Find all factors and the prime factorization of a number.
Assumptions used in this calculation
- Positive integers only: Only positive whole numbers are supported; the calculator does not factor 0, negative numbers, or non-integers.
About this calculator
Finding every divisor of a number, or breaking it down into prime factors, means testing candidate divisors one at a time, and for anything beyond small numbers it's easy to miss a factor or lose track of which primes you've already pulled out. This calculator takes a positive integer and returns two related results: the complete list of divisors, found via trial division up to √n (since any factor above the square root pairs with one below it, checking further would just repeat pairs already found), and the prime factorization, found by repeatedly dividing out the smallest prime that still divides the remainder until only 1 is left, shown in exponent form like 2² × 3². It excludes 1 from the prime factorization since 1 isn't prime by definition, while still including it in the full divisor list. That gives both views of a number's structure in one pass, without manually testing candidate divisors up to the number itself.
Worked example
36
Result: Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. Prime factorization: 2² × 3²
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