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Prime Factorization Calculator

Enter a whole number from 2 up to 1,000,000,000,000. You get its prime factors, whether it is prime, the number of divisors and the sum of the divisors.

Your numbers

Result

How we calculate it

The calculator divides the number by 2, then by each odd number in turn, up to the square root of what is left. Each time a number divides evenly it is a prime factor. Whatever is left at the end, if it is above 1, is also prime.

If n = p1^e1 × p2^e2 × …, the number of divisors is (e1 + 1) × (e2 + 1) × … and the sum of divisors is the product of (1 + p + p^2 + … + p^e) for each prime. For 360 = 2^3 × 3^2 × 5 there are 4 × 3 × 2 = 24 divisors, and their sum is 15 × 13 × 6 = 1,170.

Assumptions and limits

  • The number must be a whole number between 2 and 1,000,000,000,000. The limit keeps the answer instant in your browser.
  • 1 is not a prime number and has no prime factorization.
  • Very large numbers with two huge prime factors take the most time to factor.

Frequently asked questions

What is a prime number?

A prime number is a whole number above 1 whose only divisors are 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13.

What is prime factorization used for?

It is used to find the greatest common factor and least common multiple, to simplify fractions and roots, and to count divisors.

How do I check if a number is prime?

Enter it here. If the result shows one prime factor with an exponent of 1, the number is prime. The Is it prime? line says Yes or No.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Whole number (2 to 1,000,000,000,000) = 360.

  • Prime factorization 2^3 × 3^2 × 5
  • Is it prime? No
  • Number of divisors 24
  • Sum of divisors 1,170

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.