Prime Factorization Calculator
Quick answer: Enter any integer ≥ 2 to find its prime factors, exponential form, and divisor count.
Find the complete prime factorization of any positive integer. Enter any number and instantly see all prime factors, their exponential form (e.g., 2³ × 3 × 5), and the total number of divisors.
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Last reviewed: April 2026Report an error
Prime Factorization
2^3 × 3^2 × 5
360 = 2^3 × 3^2 × 5. 3 unique prime factor(s). Number of divisors: 24.
Factor List
2 × 2 × 2 × 3 × 3 × 5
Exponential Form
2^3 × 3^2 × 5
Number of Divisors
24
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How to Use This Prime Factorization Calculator
- 1Enter an integer (2 or greater).
- 2Read the prime factors listed individually.
- 3See the exponential form (e.g., 2³ × 3²).
- 4Note whether the number is prime and how many divisors it has.
Frequently Asked Questions
- Every integer ≥ 2 can be written as a unique product of prime numbers. 360 = 2³ × 3² × 5. This is the Fundamental Theorem of Arithmetic.
- Trial division: divide by 2, then 3, then every odd number up to √n. Each successful division gives you a prime factor.
- If n = p₁^a × p₂^b × ..., then divisors = (a+1)(b+1).... Example: 360 = 2³×3²×5 → (3+1)(2+1)(1+1) = 24 divisors.
- A prime has exactly 2 divisors: 1 and itself. 2, 3, 5, 7, 11, 13... are prime. 1 is not prime.
- GCF = product of shared prime factors at lowest exponents. LCM = product of all prime factors at highest exponents.
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