Break any positive integer into its prime factors, then see all divisors, the divisor count, the sum of divisors and whether the number is prime. Free and instant.

Enter any whole number from 2 upward.

Prime factorization
Is it prime?
Number of divisors
Sum of divisors
All divisors
Found by trial division. The factorization is shown with exponents, for example 2² × 3² × 5 for 180.

About Prime Factorization Calculator

The prime factorization calculator breaks any whole number from 2 upward into its prime factors and shows the result in exponent form, such as 2² × 3² × 5 for 180. It also tells you whether the number itself is prime, so it doubles as a quick prime checker.

The tool works by trial division: it divides your number by successive primes until only 1 remains, collecting each prime and its exponent along the way. From that factorization it derives the complete list of divisors, the divisor count and the sum of divisors.

Prime factorization comes up in math homework, simplifying fractions, finding greatest common factors and understanding how numbers are built. This calculator is free and runs entirely in your browser, so results appear the instant you type.

How to use Prime Factorization Calculator

  1. Enter any whole number from 2 upward in the number field.
  2. Or click one of the quick examples to load a sample value.
  3. Read the prime factorization shown with exponents, plus the prime check.
  4. Review the divisor count, the sum of divisors and the full list of all divisors.

Frequently asked questions

It is the unique way of writing a whole number as a product of prime numbers. For example, 180 = 2² × 3² × 5. Every integer greater than 1 has exactly one prime factorization, a fact known as the fundamental theorem of arithmetic.

It uses trial division: the number is divided repeatedly by 2, then by odd candidates, recording each prime that divides evenly until the remaining quotient is 1. This is exact for every number the tool accepts.

Yes. Trial division has a safety ceiling of 10^15 (one quadrillion). Numbers beyond that show a “too large to factor” notice instead of an incorrect or frozen result.

Both come from the factorization. If a number is p^a × q^b, it has (a+1)(b+1) divisors, and the sum of divisors follows a similar product formula. The tool also lists every divisor explicitly.

Yes. If the factorization contains only the number itself, the “Is it prime?” row shows Yes. A prime has exactly two divisors: 1 and itself.

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