Prime Factorization Calculator
Break any number into its prime building blocks.
Enter 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
- 15040 = 2^4 × 3^2 × 5 × 7
Quick answer
Every integer above 1 has a unique prime factorisation — the fundamental theorem of arithmetic.
How to use the Prime Factorization Calculator
- 1Enter any whole number above 1.
- 2Read the prime factorisation.
- 3Check the divisor list and count.
Worked example
Using the values the calculator loads with:
Inputs
- Number5040
Results
- 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
- 5040 = 2^4 × 3^2 × 5 × 7
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
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.