Prime Factorization Calculator
Enter a whole number to write it as a product of prime numbers.
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What prime factorization is
Every whole number greater than 1 is either prime (divisible only by 1 and itself) or can be written in exactly one way as a product of primes. For example 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5. This uniqueness is called the fundamental theorem of arithmetic.
How it is found
The number is divided by 2 for as long as possible, then by 3, 5, 7 and so on up to its square root. Whatever is left above 1 is itself prime. That is the same "factor tree" method taught in school, done quickly.
Uses
- LCM and HCF/GCD: compare the prime factors of two numbers, or use the LCM & GCD Calculator.
- Simplifying fractions and square roots: √72 = √(2³ × 3²) = 6√2.
- Number of divisors: add 1 to each exponent and multiply. 360 has (3+1)(2+1)(1+1) = 24 divisors.
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Runs in your browserNothing you enter is sent to a server.
Works on mobileSame tool on your phone, tablet or desktop.
How it works
- Enter — type or paste your values or text.
- Get the result — it is worked out in your browser.
- Adjust — change the inputs to compare, or copy the result.
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