MathematicsNumber Theory
Prime Number Checker & Factorization Tool
Instantly check if any integer is prime or composite. Generates complete prime factor tree, factor count, and finds the next closest prime.
Integer Primality Test
Primality Verdict
COMPOSITE
360 has multiple prime factors.
Prime Factorization:
2 × 2 × 2 × 3 × 3 × 5
Next Closest Prime:367
Mathematical Formula: Fundamental Theorem of Arithmetic
n = p₁ᵃ¹ · p₂ᵃ² ··· pₖᵃᵏ
Every integer greater than 1 either is prime itself or can be represented uniquely as a product of prime numbers.
How to Use This Calculator
- 1Enter any positive whole integer.
- 2Click Test Primality.
- 3View whether the number is Prime or Composite, its full prime factorization, and the next prime number.
Practical Example: Testing 360
Scenario: n = 360
Number:360
Result: Composite | Prime Factors: 2 × 2 × 2 × 3 × 3 × 5 (2³ × 3² × 5) | Next Prime: 367
360 is divisible by 2, 3, and 5.
Frequently Asked Questions
By definition, a prime number must have exactly two distinct positive divisors: 1 and itself. Since 1 has only one divisor (1), it is not prime.
Pro Calculation Tips
- 2 is the only even prime number; 0 and 1 are neither prime nor composite.
Model Assumptions
- Limited to safe JavaScript integer range (up to 9,007,199,254,740,991).