Prime Factorization Calculator

    Break an integer into prime factors, see repeated factors, canonical exponent form, trial-division steps, and the total number of positive factors.

    Prime factorization with steps

    English search intent for a prime factorization calculator expects the prime factors of an integer plus enough steps to check the work. Competitor pages commonly include repeated factors, exponent form, and factor-tree or trial-division style explanations.

    The same prime may appear more than once. Repeated primes are combined into exponents in canonical form.

    1. Enter one whole number of 2 or greater.
    2. Use commas or spaces as thousands separators if needed.
    3. Read the repeated factors and exponent form before using the result for GCD, LCM, or divisibility work.

    What the outputs mean

    OutputMeaning
    Prime factorizationThe product of prime numbers that equals the input
    Factors with repeatsEvery prime factor written once for each occurrence
    Distinct prime factorsHow many different primes appear
    Total positive factorsThe number of positive divisors implied by the exponents
    Prime factorization is unique for every integer greater than 1, except for the order of the factors.

    Frequently Asked Questions

    Sources and References

    Calculations are based on the listed reference sources. Links open in a new tab.

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