Prime Factorization Calculator
Break any number into its prime building blocks.
Enter your values
Enter the number you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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.
At a glance
| What it does | Break any number into its prime building blocks. |
|---|---|
| Category | Math |
| Inputs needed | Number |
| Main output | Prime factorisation |
| Cost | Free — no sign-up, no download |
How to use the Prime Factorization Calculator
- 1Enter any whole number above 1.
- 2Read the prime factorisation.
- 3Check the divisor list and count.
Inputs explained
- Number
- Enter the number you are working with.
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.
What do I need to enter into the Prime Factorization Calculator?
Just 1 value: number. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Prime Factorization Calculator work out the answer?
Every integer above 1 has a unique prime factorisation — the fundamental theorem of arithmetic. The working is shown step by step so you can verify the result by hand.
Is the Prime Factorization Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.