Prime Factorization CalculatorFree online math calculator — instant results, no sign-up
Break a number into prime factors.
About the Prime Factorization Calculator
This calculator determines the prime factorization of an integer by decomposing it into its constituent prime building blocks. It displays the complete list of prime factors multiplied together and identifies whether the input itself is a prime number.
- Number
- The positive integer to factor (typically an integer 2 or greater).
Formula and method
x = p_1 × p_2 × p_3 × ... × p_k
- xThe input integer to be factored
- p_iPrime factor dividing x, where each p_i is a prime number (p_1 ≤ p_2 ≤ ... ≤ p_k)
- kTotal count of prime factors (multiplicity included)
The tool repeatedly extracts prime factors from the integer x using trial division until the quotient is reduced to 1. The resulting factors are formatted as a multiplication sequence joined by '×', and if the factor list contains exactly one element, the number is identified as prime.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Number360
Results
- Prime factors2 × 2 × 2 × 3 × 3 × 5
- Is primeNo
How to use the Prime Factorization Calculator
- 1Enter an integer into the Number field.
- 2The algorithm divides the number by the smallest possible prime factor (starting at 2).
- 3It continues dividing intermediate quotients by primes until reaching 1, collecting all prime divisors.
- 4The tool outputs the full product of prime factors and displays 'Yes' if the number has exactly one factor (itself), or 'No' otherwise.
Reading your result
The 'Prime factors' field lists all prime numbers whose product equals the input value, showing repeated factors explicitly. The 'Is prime' field indicates 'Yes' if the integer is greater than 1 and only divisible by 1 and itself, or 'No' if it is composite.
Limitations
The calculator is designed for standard positive integers; non-integer decimals, negative numbers, and 0 or 1 do not have standard prime factorizations. In addition, extremely large numbers (beyond standard JavaScript safe integer limits of 2^53 - 1) cannot be factored accurately in the browser.
Common questions
Why is the number 1 not considered a prime number?+
By definition in mathematics (the Fundamental Theorem of Arithmetic), a prime number must have exactly two distinct positive divisors: 1 and itself. The number 1 has only one divisor, so it is neither prime nor composite.
What is the difference between prime factors and unique prime factors?+
Prime factors include multiplicity (for example, 360 = 2 × 2 × 2 × 3 × 3 × 5, which has six prime factors total), whereas unique prime factors list each distinct base only once (2, 3, and 5).
How does prime factorization help find the greatest common divisor (GCD)?+
Once two numbers are broken into their prime factorizations, their GCD is simply the product of the lowest powers of all prime factors they share in common.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.