Factor Calculator
Every factor of a number, plus its prime factorization
Frequently Asked Questions
Finding every factor of a number, and separately its prime factorization, are two related but distinct outputs — the full factor list includes every number that divides evenly into the target, while prime factorization specifically breaks the number down into the unique combination of prime numbers that multiply together to produce it.
Why full factors and prime factorization are different (but related) results
Every positive integer greater than 1 has a complete factor list — every whole number that divides into it with no remainder, including 1 and the number itself. Separately, every such integer also has a unique prime factorization — a specific combination of prime numbers (numbers divisible only by 1 and themselves) that, multiplied together, produce the original number; this decomposition is unique for any given number (a mathematical fact known as the fundamental theorem of arithmetic), unlike the full factor list, which can be derived in multiple ways but always converges on the same complete set. Prime factorization is the more fundamental of the two in a mathematical sense, since every other factor of the number can be derived by combining subsets of its prime factors, while the reverse isn't true.
A worked example
A number's full factor list can be substantially longer than its prime factorization, since the full list includes every combination of the prime factors multiplied together (including 1 and the number itself), while the prime factorization lists only the irreducible prime building blocks — the two outputs answer related but genuinely different questions about the same number's structure.
How this connects to your other math calculations
Prime factorization is the foundation for finding the LCM/GCF (least common multiple and greatest common factor) of two or more numbers — both of those calculations are built directly from comparing the prime factorizations of the numbers involved, which is exactly why this calculator's output feeds naturally into that related calculation.
Common mistakes
Confusing "factors" with "prime factors" — reporting only the prime factorization when the full factor list was actually needed, or vice versa — is a common terminology mix-up, since the two terms sound similar but describe genuinely different (though related) outputs for the same number.