Prime Factorization Calculator
Break a whole number into its prime factors, shown with exponents and as a full product. Calculates in your browser.
Prime factorization
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Show the math
Divide by the smallest prime that fits, repeating until only 1 remains:
360 = 2³ × 3² × 5
Every integer above 1 has exactly one prime factorization. Repeated factors are gathered into exponents, and a prime number factorizes to just itself. All math runs locally in your browser.
What this does
A prime factorization calculator breaks a whole number down into the prime numbers that multiply together to make it. Every integer above 1 has exactly one prime factorization.
How to use it
- Enter a whole number greater than 1.
- Read its prime factors with exponents.
- See the full product written out.
How it works
The calculator divides by the smallest prime that fits, repeating until only 1 remains. Repeated factors are gathered into exponents. A prime number factorizes to just itself.
360 = 2³ × 3² × 5
Understanding your result
The prime factorization is the unique "fingerprint" of a number, the building blocks that no further factoring can break down. It is the basis for finding the greatest common factor and least common multiple, and a number that factorizes to just itself is prime. The fundamental theorem of arithmetic guarantees this breakdown is the only one.
Example
360 = 2³ × 3² × 5, while 17 is prime, so its only factorization is 17 itself.
Sources & methodology
Last updated .
Frequently asked questions
What is prime factorization?
It is writing a number as a product of prime numbers, primes being whole numbers above 1 divisible only by 1 and themselves. For 12 it is 2 × 2 × 3, or 2² × 3.
What if the number is prime?
A prime number has no smaller prime factors, so its factorization is just the number itself, such as 13 = 13.
Why is prime factorization unique?
The fundamental theorem of arithmetic guarantees every integer above 1 has exactly one set of prime factors, regardless of the order you find them in.
Is my data stored?
No. Everything is calculated locally in your browser.
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