Prime Factorization
Factor an integer at least 2 with up to 15 digits. Check product and exponent forms, positive divisor count and primality. Press Factorize or Enter to run.
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Enter an integer and press Factorize.
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Prime Factorization
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How to use
- 1
Enter a number
Type an integer at least 2 with up to 15 digits, then press Factorize or Enter (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).
Trial division of 360 gives three factors of 2, two of 3 and one of 5. Tests need only reach the square root of the remaining quotient, but large primes can require more trials. The 15-digit input limit is not a speed guarantee.
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?
1 has no prime factors and this tool starts at 2. The prime 2 is displayed as itself.
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?
From 2 to 999,999,999,999,999. Even within 15 digits, processing time depends on factor sizes. Editing clears the old result; press Factorize or Enter to run again.
Related guide
GuideHow to Use the Laws of Exponents: Product, Quotient, Power and More
Compare exponent laws, negative bases and reciprocals. Distinguish −2⁴ from (−2)⁴, understand the 0⁰ convention, fractional-exponent limits, scientific notation for 10⁻⁷ and exact versus approximate calculation.
GuideHow to Do Prime Factorization
Factor 360 with a step diagram and comparison tables. Verify product and exponent forms, derive 24 positive divisors, choose GCD/LCM or fraction tools, and check the 15-digit input limit and recalculation workflow.
GuideArithmetic and Geometric Series: How to Find the Sum of a Sequence
Compare arithmetic and geometric terms and sums with worked tables. Count terms correctly, handle r=1 and negative ratios, separate finite and infinite sums, and verify integer versus decimal calculator limits.
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Verified: Factorization, exponent form, divisor count, prime detection and error states are covered by browser tests