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Math & statistics

Prime factorization

Decompose a positive whole number into prime factors, exponents and the number of positive divisors.

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How it works

Trial divide by 2, then odd divisors up to the square root of the remaining factor; combine equal factors.

Input definitions

Integer from 2 to 1,000,000,000,000
Enter the value in the labeled unit.

A worked example

Integer from 2 to 1,000,000,000,000
360
2^3 × 3^2 × 5

Assumptions & limits

Mathematical calculation using the stated inputs; not a measurement guarantee.

Sources & review

Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.

Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.

Common questions

Why can statistical results differ between tools?

Denominator, interpolation and boundary conventions can differ. Use the method and assumptions on this page to compare the same definition; displayed decimals may also be rounded.

How does the Prime factorization tool work?

Trial divide by 2, then odd divisors up to the square root of the remaining factor; combine equal factors.

What are the assumptions and limits of Prime factorization?

Mathematical calculation using the stated inputs; not a measurement guarantee.

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