Prime Factorization Tool
Break any positive integer into its prime factors. See factor list, exponent form, and total divisor count.
Results
Prime Factors (with repetition)
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Exponent Form
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Number of Divisors
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Is Prime?
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About Prime Factorization
Prime factorization rewrites an integer as a product of prime numbers. This decomposition is unique (Fundamental Theorem of Arithmetic), which makes it useful in number theory, simplification, divisibility checks, and cryptography fundamentals.
How to Use
- Enter a positive integer in the input field.
- Click Factorize — results appear instantly.
- View the prime factors as a product list, in exponent form, and see the total divisor count.
How It Works
The tool uses trial division: it repeatedly divides the input by the smallest prime factor starting from 2. Each time a factor divides evenly, it is recorded and the quotient continues. This repeats until the remaining quotient is 1.
Example
360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5
Total divisors of 360 = (3+1) × (2+1) × (1+1) = 4 × 3 × 2 = 24.
Frequently Asked Questions
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
No. By mathematical convention, 1 is neither prime nor composite. Prime factorization applies to integers greater than 1.
The tool handles numbers up to several million quickly using trial division. Very large numbers (millions of digits) require specialized algorithms and are beyond the scope of this browser tool.
If the prime factorization is p1^a1 × p2^a2 × ..., the total number of divisors is (a1+1) × (a2+1) × ... This counts all numbers that divide evenly into the original, including 1 and itself.