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How to use
Every integer above 1 has a unique prime-factor product apart from factor order. The tool uses trial division and returns the factors, exponent form and divisor count.
- Enter an integer from 2 to 10^12.
- Factor it.
- Review prime factors and exponent form.
- Review distinct-factor count, divisor count and prime/composite status.
How it is calculated
Example
Factor 360 by dividing repeatedly: 360÷2=180, 180÷2=90, 90÷2=45, 45÷3=15, and 15÷3=5. This gives 360=2³×3²×5. A positive divisor can use exponents 0 through 3 for 2, 0 through 2 for 3, and 0 through 1 for 5, so there are (3+1)×(2+1)×(1+1)=24 divisors.
Important notes
The calculator accepts safe integers only within the stated limit. Larger integers can require more specialized factorization algorithms.
Worked examples and interpreting results
The prime factorization of 60 is 2²×3×5. Exponent 2 means that prime 2 occurs twice. The exponents show that there are 12 positive divisors, including 1 and the number itself.
| Case | Calculation | Result |
|---|---|---|
| Reconstruct from prime factors | 2² × 3 × 5 | 60 |
| Positive divisor count | (2 + 1) × (1 + 1) × (1 + 1) | 12 |
How to check the result
Every final factor must be prime: 4×15 is a factorization but not a completed prime factorization. One is not prime, and zero has no finite prime factorization of this kind.
Frequently asked questions
Does a prime number have a factorization?
Yes: the number itself to exponent 1.
Why use exponent form?
It compresses repeated factors such as 2×2×2 into 2³.
How is divisor count found?
From the exponents: ∏(eᵢ+1).
Is prime factorization unique?
Yes. Every integer greater than 1 has one prime factorization apart from factor order. Factors may repeat, commonly written with exponents, for example 12=2²×3.