Prime Factorizer
Enter any number to check if it's prime. If it's not, see its complete prime factorization with exponents, plus a list of all factors.
Up to 1,000,000,000,000
How it works
The tool uses trial division to find prime factors. It starts by dividing out all 2s, then tests odd numbers up to the square root of the remaining value. If a divisor is found, it's recorded and divided out repeatedly until it no longer divides evenly, then the search continues with the next candidate.
The result is displayed as a product of prime powers — for example, 360 = 2³ × 3² × 5. A complete list of all divisors (not just prime ones) is also generated by combining every possible subset of the prime factors.
Prime factorization is fundamental in number theory and has practical applications in cryptography, greatest common divisor calculations, and simplifying fractions. This tool handles numbers up to the limits of JavaScript's safe integer range.