Break a number down into the prime numbers that multiply together to produce it, shown as a plain list and in compact exponent form.
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Every whole number greater than 1 can be broken down into a unique product of prime numbers, this is known as the Fundamental Theorem of Arithmetic. This calculator finds that breakdown by repeatedly dividing by the smallest possible prime until only 1 remains, then shows the result both as a plain multiplication list (e.g. 2 × 2 × 2 × 3 × 3 × 5) and in the more compact exponent form (2^3 × 3^2 × 5) used when a prime factor repeats.
Prime factorization is the basis for finding a number's GCF and LCM with other numbers, simplifying fractions, and various topics in number theory and cryptography. It's also a common way to check whether a number is 'nice' for a particular calculation, for example, a number with only small prime factors divides evenly by many things.
The factorization of a prime number is just the number itself, since it has no smaller prime factors, this calculator will show it as a single factor.
The Prime Number Calculator checks whether a number is prime and also finds its nearest primes, with factorization as one of several outputs. This calculator is purpose-built around factorization specifically, presenting it both as a list and in the more standard exponent notation.
This calculator supports numbers up to 100,000,000. Beyond that, factorization by trial division becomes impractically slow.
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