Prime Factorization Calculator
Breaks a number into its prime factors, with how many divisors it has and what they add up to.
Results
What this tool does
Every whole number above one is a product of primes in exactly one way — that is the fundamental theorem of arithmetic, and it is why primes are called the building blocks of number. Finding the factors is what makes simplifying a fraction, finding a lowest common denominator or reducing a gear ratio straightforward rather than guesswork. The count and the sum of the divisors come out of the same decomposition, without anything being listed.
Formula
divides repeatedly by the primes until 1 is left
Variables
| Symbol | Meaning | Unit |
|---|---|---|
number | Number | — |
FA | Prime factorisation | — |
FT | Factors counted with repeats | — |
DV | Number of divisors | — |
DS | Sum of the divisors | — |
Worked example
- Number360
- Prime factorisation2 x 2 x 2 x 3 x 3 x 5
- Factors counted with repeats6
- Number of divisors24
- Sum of the divisors1170
Limitations
- The calculation runs entirely in your browser. The values you type are never sent to a server.
Frequently asked questions
How is the number of divisors worked out?
From the exponents, not by counting. Once you know that 360 is 2³ × 3² × 5, every divisor is made by choosing how many 2s to take (0 to 3, so four choices), how many 3s (three choices) and how many 5s (two choices): 4 × 3 × 2 = 24 divisors, without ever listing one. The sum of the divisors follows from the same decomposition.