Prime Factorisation Calculator
Factor Tree & Index Form ⚡
Enter any positive integer to find its prime factorisation, displayed as a factor tree and in index notation.
Enter any positive integer to find its prime factorisation, displayed as a factor tree and in index notation.
Prime factorisation breaks a number down into its prime number building blocks. Every positive integer greater than 1 is either prime itself, or can be expressed as a unique product of prime numbers — this is the Fundamental Theorem of Arithmetic. For example, 360 = 2³ × 3² × 5.
What is a prime number?
A prime number is a positive integer greater than 1 that has no factors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23...
Is 1 a prime number?
No. By convention, 1 is neither prime nor composite. Prime factorisation requires numbers of 2 or greater.
What is index notation?
Index notation (also called exponential notation) writes repeated prime factors as a power. For example, 2 × 2 × 2 is written as 2³. This is the standard way to express a prime factorisation.
What is the largest number I can factorise?
This calculator works for any integer up to JavaScript's safe integer limit (2⁵³). For very large numbers the calculation may take a moment.