How to factor a whole number
Enter a whole number from 2 through 999,999,999,999,999. The calculator returns its prime factorization, separates distinct primes from repeated factors, and shows the recorded division steps.
What the result shows
After a valid calculation, review these fields:
- Number: the value you entered.
- Prime factorization: the factorization using exponents for repeated prime factors.
- Distinct primes: the number of different prime factors.
- Total factors (with multiplicity): the total count when repeated factors are counted separately.
- Is prime? whether the entered number itself is prime.
Factor chips show each distinct prime, with an exponent when it is greater than 1. Open Formula & steps to see the starting value, successful divisor reductions, and the conclusion about any remaining prime value. Failed candidate checks are not listed.
Use Copy result to copy the plain-text result to the browser clipboard. Use Download result (.txt) to save it as prime-factorization-calculator-result.txt.
How to use the calculator
- Enter a value in Whole number to factor.
- Select Calculate, or press Enter.
- Review the result fields, factor chips, and Formula & steps.
- Select Reset to clear the input and hide the result.
Accepted and rejected input
The calculator accepts one whole number from 2 through 999,999,999,999,999. It trims leading and trailing whitespace and accepts an optional leading plus sign. Values below 2, negative numbers, fractions, decimals, and other non-digit characters are rejected. Invalid input displays an error and hides the result section.
How the calculation works
The calculation runs in the page's JavaScript. It divides by 2 first, then tests successive odd candidates while the candidate is within the current square-root bound.
while p × p ≤ remaining: if remaining mod p = 0, divide remaining by p and record p
When no candidate up to √remaining divides evenly, any remaining value greater than 1 is recorded as prime. The factorization uses this form:
n = p1e1 × p2e2 × ... × pkek
Each p is a distinct prime, and each exponent e records how many times it divides the number. The calculation uses exact integer arithmetic for the supported range.
Limitations and calculation privacy
The upper limit is 999,999,999,999,999. The tool accepts a single whole number only; it does not factor negative numbers, fractions, decimals, or expressions. The entered value is processed locally by the page's JavaScript, and the calculation script contains no upload call.
Frequently Asked Questions
What is prime factorization?
Prime factorization writes an integer as a product of prime numbers. For example, 60 = 22 × 3 × 5.
How is prime factorization calculated?
The calculator divides by 2, then tests successive odd candidates up to the current square-root bound. It records successful divisions and, when appropriate, the remaining value as a prime. Failed candidate checks are not displayed.
Is 1 a prime number?
No. The number 1 has only one divisor, so it is neither prime nor composite and has no prime factorization. This calculator requires an input of 2 or greater.
How do I know if a number is prime from this calculator?
Check Is prime? in the result. A prime input also appears as one distinct factor with exponent 1.
What is the largest number this calculator can factor?
The largest supported value is 999,999,999,999,999. Larger values are rejected.