Prime Factorization Calculator (Factor Tree, Free)

Use this free prime factorization calculator to break any whole number into its prime factors. Enter a number and you’ll get the factorization in exponent form (like 360 = 2³ × 3² × 5), whether the number is prime, how many divisors it has, and the full list of its factors — with the division steps shown.

How to use the calculator

1. Enter a whole number (2 or greater).
2. Press Calculate.
3. Read the prime factorization, the divisor count, and every factor, with the step-by-step working.

What is prime factorization?

Prime factorization writes a number as a product of prime numbers. You divide repeatedly by the smallest prime that fits, then collect repeated primes as exponents. It’s the key to simplifying fractions and finding GCF and LCM.

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Frequently asked questions

How do you find the prime factorization of a number?

Divide by the smallest prime that goes in evenly, then keep dividing the result the same way until you reach 1. Collect repeated primes as powers.

How many divisors does a number have?

Add one to each exponent in the prime factorization and multiply: 360 = 2³·3²·5 has (3+1)(2+1)(1+1) = 24 divisors.

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How can I tell if a number is prime?

If its only factors are 1 and itself, it’s prime. The calculator tells you directly and, if not prime, lists the prime factors.

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Read the full lesson: learn the method step by step.

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