When to use this calculator
Decompose a positive integer into its prime factors. Repeated prime factors are listed separately rather than shown as exponent notation.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Prime Number Checker: Check whether an integer is prime using exact trial division within the supported range.
PUTTING IT INTO PRACTICE
Prime Factorization: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Whole number (integer) | 360 |
| Result | 2 × 2 × 2 × 3 × 3 × 5 |
- Check the input labels and enter the example values above.
- Apply the relationship: Repeatedly divide by prime factors until the remaining factor is prime..
- The result is 2 × 2 × 2 × 3 × 3 × 5 , rounded for display.
How to interpret your result
Repeated prime factors are listed separately rather than shown as exponent notation.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the prime factorization calculator useful?
Decompose a positive integer into its prime factors. Repeated prime factors are listed separately rather than shown as exponent notation.
How do I use the prime factorization calculator?
Enter whole number (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Repeatedly divide by prime factors until the remaining factor is prime..
What should I check before using the result?
Repeated prime factors are listed separately rather than shown as exponent notation.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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