Math

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.

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.

At a glance

What it doesBreak any number into its prime building blocks.
CategoryMath
Inputs neededNumber
Main outputPrime factorisation
CostFree — no sign-up, no download

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.

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
  1. 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.