Why does trial division only go up to the square root of n?

Any factor of n larger than √n must be paired with a factor smaller than √n, so checking divisors up to √n and recording both members of each pair finds every factor without redundant work.

Is 1 counted as a prime factor?

No. By definition a prime number is greater than 1 with exactly two divisors, so 1 is never included in the prime factorization, only in the full list of divisors.

Factors & Prime Factorization Calculator

Find all factors and the prime factorization of a number.

How this is calculated

Trial division up to √n for both the full divisor list and the prime factorization

Assumptions used in this calculation

Positive integers only: Only positive whole numbers are supported; the calculator does not factor 0, negative numbers, or non-integers.

About this calculator

Lists all divisors and the prime factorization of a positive integer, consolidating the master prompt's separate 'Factor Calculator' and 'Prime Factorization Calculator' into one page, since both describe the same number.

Worked example

Result: Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. Prime factorization: 2² × 3²

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Frequently asked questions

GCF & LCM Calculator

Find the greatest common factor and least common multiple of two or more numbers.

Factors & Prime Factorization Calculator

About this calculator

Frequently asked questions

Why does trial division only go up to the square root of n?

Is 1 counted as a prime factor?

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