Why Use This Tool?
Prime numbers are the atoms of arithmetic — every integer is a unique product of them. This tool checks primality with efficient trial division (only testing up to the square root), breaks any number into its complete prime factorization, and lists primes in a range.
Factorization answers the question 'what multiplies to make this number', which is the foundation of simplifying fractions, finding common denominators, and cryptography basics.
How It Works
- Enter a number to check primality and see its factors.
- Or set a range to list every prime within it.
- Read the factorization — primes show themselves as single-term products.
Frequently Asked Questions
How do I check if a number is prime?
Test divisibility by every number up to its square root — if none divide evenly, it's prime. The tool applies this with the 6k±1 optimization, so even large numbers check instantly.
What is prime factorization?
Breaking a number into the primes that multiply to it: 360 = 2 × 2 × 2 × 3 × 3 × 5. Every integer above 1 has exactly one such factorization.
Why is 1 not a prime number?
Primes must have exactly two distinct divisors. 1 divides only by itself, so counting it as prime would break the uniqueness of factorization.
Tips & Things to Watch
- 91 looks prime but equals 7 × 13 — always check, never assume.
- The square-root shortcut is why checking a million-digit range stays fast.
- Factorizations pair naturally with the fraction calculator for simplifying.