Prime Factorization Calculator
Find all prime factors of a number with factor tree visualization and exponent notation.
Number & mode
Updates as you typeMode
What do you want to do? ?
Number
Value ?
—
Second number ?
—
Try an example
Factor table
—| Prime | Power | Expression | Value |
|---|
All divisors
—Factor tree
Each branch splits to its smallest prime factor.GCD & LCM
—GCD
—
—
LCM
—
—
Coprime?
—
—
Formula
n
=
p1a1
·
p2a2
·
…
·
pkak
- n
- The integer being factorized (≥ 2)
- pi
- A distinct prime factor of n
- ai
- The multiplicity of pᵢ (how many times it divides n)
- τ(n)
- Divisor count — (a₁+1)(a₂+1)…(aₖ+1)
- σ(n)
- Divisor sum — ∏ᵢ (pᵢ^(aᵢ+1)−1) / (pᵢ−1)
Worked example — your number
- Start with —
- Trial-divide by primes 2, 3, 5, 7, … collecting each that divides in.
- Prime factors found: —
- Factorization: —
- τ = — · σ = —
The Fundamental Theorem of Arithmetic guarantees that every integer greater than 1 has exactly one prime factorization — up to the order of the factors. Trial division works well for the numbers in this tool; for very large integers, algorithms like Pollard's rho or the general number field sieve take over.