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Factor Calculator

List all positive factors, factor pairs, and the prime factorization of a whole number.

General

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How it works

A factor of n is a positive integer d such that n is evenly divisible by d. Prime factorization multiplies primes to recover n; factor trees peel smallest primes step by step.

d | n ⇔ n % d = 0 · n = p₁ × p₂ × …

When to use

Use this tool when you need to: try 120 for the classic tree (2×2×2×3×5), or 30 for factors 1, 2, 3, 5, 6, 10, 15, 30. Related: LCM and GCF.

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Try 120 for the classic tree (2×2×2×3×5), or 30 for factors 1, 2, 3, 5, 6, 10, 15, 30. Related: LCM and GCF.

Frequently asked questions

What is the Factor Calculator?
A factor of n is a positive integer d such that n is evenly divisible by d. Prime factorization multiplies primes to recover n; factor trees peel smallest primes step by step.
How do I use the Factor Calculator?
Enter the required values, then calculate. The Factor Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Factor Calculator use?
d | n ⇔ n % d = 0 · n = p₁ × p₂ × …

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Factor calculator

Enter a non-zero integer to list every positive factor, factor pairs that multiply back to the number, and its prime factorization.

Whole numbers only. Negatives use the absolute value for factor lists. Zero is not allowed (infinitely many divisors).

Try an example

How it works

What is a factor?

In multiplication, factors are the integers that are multiplied together to find other integers. For example, 6 × 5 = 30 — so 6 and 5 are factors of 30. The full positive factor list of 30 is 1, 2, 3, 5, 6, 10, 15, and 30. Essentially, an integer a is a factor of another integer b when b can be divided by a with no remainder. Factors matter for fractions, simplifying expressions, and spotting patterns in numbers. Every positive factor appears in a pair (d, n/d) that multiplies back to |n|. Zero is excluded because it has infinitely many divisors.

Prime factorization

Prime factorization finds the prime numbers that, when multiplied, return the original number. For example, 120 = 2 × 2 × 2 × 3 × 5 (compact form 2³ × 3 × 5). By the fundamental theorem of arithmetic, every integer greater than 1 has a unique prime factorization (order aside). Very large integers can make factoring by hand tedious; there is no known general algorithm that is efficient for all huge composites, which is why cryptographic challenges use very large products of primes.

Factor trees

A factor tree splits a composite number into a prime and a cofactor, then continues on any remaining composite branch until only primes remain. Example for 120: 120 = 2 × 60 60 = 2 × 30 30 = 2 × 15 15 = 3 × 5 Multiplying the leaf primes gives 2 × 2 × 2 × 3 × 5 = 120. This calculator peels the smallest prime at each step and shows the same work in the steps and explanation tabs.

Related calculators

LCM and GCF work from shared multiples and divisors across several integers; the prime tool focuses only on factorization; common factors lists shared divisors of a list.

  • Least Common Multiple Calculator
  • Greatest Common Factor Calculator
  • Prime Factorization Calculator
  • Common Factor Calculator