Enter any positive integer to break it down into its prime factors, shown both as a factor tree list and in exponent form.
Prime factorization breaks a number down into the set of prime numbers that multiply together to produce it. Every whole number greater than 1 has a unique prime factorization — a rule known as the Fundamental Theorem of Arithmetic. This tool calculates that factorization instantly for any number you enter.
A prime number is a whole number greater than 1 that has no divisors other than 1 and itself — examples include 2, 3, 5, 7, 11, and 13.
The calculator repeatedly divides your number by the smallest possible prime number until only prime factors remain, using a method called trial division.
Enter any whole number greater than 1 and click Calculate. The tool lists every prime factor, along with how many times each appears (its exponent).
Example 1: 60 = 2² × 3 × 5, meaning 60 = 2 × 2 × 3 × 5.
Example 2: 100 = 2² × 5² = 2 × 2 × 5 × 5.
Is 1 a prime number? No, by definition primes must have exactly two distinct divisors (1 and itself), and 1 has only one divisor.
What is prime factorization used for? It's used to simplify fractions, find the greatest common factor (GCF) and least common multiple (LCM) of numbers, and it forms the mathematical basis of modern encryption methods used to secure online transactions.
Can every number be factored into primes? Yes, every integer greater than 1 is either prime itself or can be expressed as a unique product of primes.
How many prime factors can a number have? There's no fixed limit — larger numbers generally have more prime factors, though some large numbers have very few (if they're a product of just two large primes, as used in cryptography).
Is factoring large numbers hard for computers? Factoring small to moderately sized numbers is fast, but factoring extremely large numbers (hundreds of digits) is computationally difficult, which is exactly why it's used in encryption security.