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Calculation Machine

Prime Factorization Calculator

Break any number into its prime building blocks.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Prime factorisation
2^4 × 3^2 × 5 × 7
Is it prime?
No
Number of divisors
60
All divisors
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144

Working

  1. 15040 = 2^4 × 3^2 × 5 × 7

Quick answer

Every integer above 1 has a unique prime factorisation — the fundamental theorem of arithmetic.

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Number5040

Result

  • Prime factorisation2^4 × 3^2 × 5 × 7
  • Is it prime?No
  • Number of divisors60
  • All divisors1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144

How to use the Prime Factorization Calculator

  1. 1Enter any whole number above 1.
  2. 2Read the prime factorisation.
  3. 3Check the divisor list and count.

Frequently asked questions

Why is 1 not prime?

Primes have exactly two distinct divisors. 1 has only one, and treating it as prime would break unique factorisation.

What is the largest known prime?

As of 2024 it is 2^136,279,841 − 1, a Mersenne prime with over 41 million digits.

About this calculator