Prime Factorization Calculator
Calculate prime factorization instantly in your browser.
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What this tool does
Calculate prime factorization instantly in your browser. Trial division up to √n; every whole number above 1 has exactly one prime factorization (the fundamental theorem of arithmetic).
How to use the Prime Factorization Calculator
- Enter or select whole number.
- Read the calculated result; change any measurement to compare alternatives.
Formula
Divide repeatedly by the smallest prime that divides the number (2, then 3, then 5, …) until the quotient is 1; the divisors used are the prime factorization.
- x
- Whole number
Trial division up to √n; every whole number above 1 has exactly one prime factorization (the fundamental theorem of arithmetic).
Worked example
For prime factorization calculator, the following measurements illustrate the exact method: Whole number: 360.
Inputs
- Whole number360
Result
- Prime factorization2^3 × 3^2 × 5
- Distinct prime factors2, 3, 5
- Total prime factors (with multiplicity)6
Results explained
- Prime factorization
- Prime factorization from the formula above. Trial division up to √n; every whole number above 1 has exactly one prime factorization (the fundamental theorem of arithmetic).
- Distinct prime factors
- Distinct prime factors from the formula above. Trial division up to √n; every whole number above 1 has exactly one prime factorization (the fundamental theorem of arithmetic).
- Total prime factors (with multiplicity)
- Total prime factors (with multiplicity) from the formula above. Trial division up to √n; every whole number above 1 has exactly one prime factorization (the fundamental theorem of arithmetic).
Frequently asked questions
Divide repeatedly by the smallest prime that divides the number (2, then 3, then 5, …) until the quotient is 1; the divisors used are the prime factorization.
Trial division up to √n; every whole number above 1 has exactly one prime factorization (the fundamental theorem of arithmetic).
Where mathematically meaningful, yes. Fields specify permitted ranges and undefined operations display an error.
Exact integer calculations use safe integers; decimal calculations use browser floating point, so small rounding differences can occur.
All values remain in your browser and are never uploaded.