About PrimeCalc

PrimeCalc is a free collection of number theory calculators built for students, mathematicians, developers, and curious minds. Check whether a number is prime, find its complete prime factorization, compute GCDs and LCMs, generate prime lists, and explore number patterns — all running instantly in your browser without any sign-up or fees.

Our Mission

Number theory is one of the oldest and most elegant branches of mathematics, yet most online tools for it are either buried in academic software or wrapped in cluttered interfaces. PrimeCalc's mission is to make these calculations simple and immediate: enter a number, get your answer, understand why.

Every result includes a brief explanation of the method used — not just the output, but the reasoning behind it. We believe calculators should help you learn, not just automate.

What We Offer

• Prime Checker: Instantly determine whether any integer is prime, with the factorization shown for composite numbers. Uses trial division with optimizations for speed on large inputs.
• Prime Factorization: Break any number into its complete prime factor tree. Results are displayed in both expanded form (2 × 2 × 3 × 7) and exponential form (2² × 3 × 7).
• GCD Calculator: Find the greatest common divisor of two or more numbers using the Euclidean algorithm. Useful for simplifying fractions and solving Diophantine equations.
• LCM Calculator: Find the least common multiple — essential for adding fractions, synchronizing cycles, and scheduling problems.
• Prime Number List Generator: Generate all primes up to a given limit using the Sieve of Eratosthenes. Outputs can be copied for use in code or study materials.
• Divisors & Factor Pairs: List every divisor of a number and group them into factor pairs. Useful for understanding divisibility and solving word problems.

Who Uses PrimeCalc?

• Students: Checking homework, understanding factorization steps, and exploring number patterns in math courses from middle school through university.
• Developers: Quickly verifying primality during algorithm development, generating test data, and checking modular arithmetic results.
• Puzzle solvers: Number puzzles, competition math (AMC, MATHCOUNTS, Olympiad), and recreational mathematics often require rapid prime and factor lookups.
• Teachers: Generating examples and verifying solutions for number theory lessons.

How Our Calculators Work

All calculations run directly in your browser using JavaScript. For primality testing, we use optimized trial division — checking divisibility only by odd numbers up to √n, which is correct and efficient for numbers in the typical range entered by users. The Sieve of Eratosthenes powers the prime list generator, which is significantly faster for generating ranges of primes than testing each number individually.

No data is sent to any server. Results are available instantly without page reloads.

Accuracy

PrimeCalc's algorithms are mathematically exact for integers within JavaScript's safe integer range (up to 2⁵³ − 1, or about 9 quadrillion). For typical use cases — classroom work, programming, and recreational math — this range is more than sufficient. Very large number factorizations (numbers with many digits) may be slow due to the computational nature of trial division.

Contact and Feedback

Found an error or want to suggest a new calculator? Visit our contact page. We review all submissions and prioritize bug reports.