Prime Factorization
Factor any positive integer into primes. See the product form, exponent form (e.g. 2³×3²) and the number of divisors at once.
Enter an integer and press Factorize.
Done
Prime Factorization
How to use
- 1
Enter a number
Type the positive integer you want to factor (e.g. 360).
- 2
Read the factors
The product form (2×2×2×3×3×5) and exponent form (2³×3²×5) are shown.
- 3
Check the divisors too
The number of divisors and whether the number is prime are displayed as well.
Features
- Shown in both product and exponent form
- Divisor count and prime check included
- Supports integers up to 15 digits (trial division)
- Everything computed in your browser; nothing is transmitted
Use cases
Checking homework
Verify factorization answers, including the exponent form.
Counting divisors
Use the exponents to confirm the number of divisors.
GCD and LCM preparation
Compare the factors of two numbers to find common primes for the GCD.
Details
Prime factorization means writing a positive integer as a product of prime numbers only. For example, 360 = 2×2×2×3×3×5, or 2³×3²×5 in exponent form. Every integer greater than 1 has exactly one prime factorization (the fundamental theorem of arithmetic).
The tool uses trial division: divide by the smallest prime, record each successful factor, and repeat on the quotient. For 360, dividing by 2 three times, 3 twice and 5 once gives the factors 2, 2, 2, 3, 3, 5. Testing divisors only up to the square root is enough, so even large numbers finish quickly.
Prime factorization underlies greatest common divisors, least common multiples and counting divisors. It also underpins security: the difficulty of recovering two large primes from their product is the foundation of RSA encryption. Everything runs in your browser and nothing you enter is transmitted.
FAQ
Can 1 be factored?
No. 1 is not prime and cannot be written as a product of primes, so it has no prime factors.
How is a prime number detected?
A number above 1 whose only divisors are 1 and itself is shown as prime. If the input itself is prime, that is displayed directly.
How is the number of divisors calculated?
Add 1 to each exponent and multiply: 360 = 2³×3²×5 gives (3+1)×(2+1)×(1+1) = 24 divisors.
How large a number can I enter?
Up to 15 digits. Larger numbers would take too long and show an error instead.
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Verified: Factorization, exponent form, divisor count, prime detection and error states are covered by browser tests