Prime Factorization Calculator
Calculate prime factor trees and prime factorizations for integers.
GCD & LCM Calculator
About Prime Factorization Calculator
The Prime Factorization & Factor Tree Generator decomposes any integer into its unique prime factors using Pollard's Rho algorithm and trial division, outputting exponential canonical form ($p_1^{e_1} \cdot p_2^{e_2}...$), factor trees, and divisor counts.
How to Use Prime Factorization Calculator
Step 1
Enter an integer greater than 1.
Step 2
Click "Factorize".
Step 3
Review canonical prime factorization and divisor statistics.
Step 4
Click "Copy Factorization".
Practical Use Cases for Prime Factorization Calculator
Mathematics Education & Factor Trees
Generate visual factor tree diagrams and canonical exponential forms for mathematics study and homework verification.
Number of Divisors & Sum of Divisors
Calculate the total number of divisors $\\tau(n)$ and sum of divisors $\\sigma(n)$ directly from prime factor exponents.
Input & Output Examples
Factoring 360 into Prime Factors
Number: 360
Prime Factorization: 2^3 * 3^2 * 5 | Expanded: 2 * 2 * 2 * 3 * 3 * 5 | Total Divisors: 24 | Sum of Divisors: 1170
Key Features & Performance
- ✓Outputs Canonical Exponential Form ($2^3 \\times 3^2 \\times 5$) and expanded multiplication list.
- ✓Calculates Total Divisors count ($\\tau(n) = (e_1+1)(e_2+1)...$) and Sum of Divisors ($\\sigma(n)$).
- ✓Supports BigInt numbers up to $10^{18}$ with Pollard's Rho fast factorization.
- ✓100% Client-Side calculation.
- ✓1-Click Copy factorization.
Key Terminology & Definitions
Fundamental Theorem of Arithmetic
Every integer greater than 1 either is a prime itself or can be represented as the product of prime numbers uniquely, up to the order of the factors.
Canonical Prime Factorization
Writing a number as $n = p_1^{a_1} p_2^{a_2} \\dots p_k^{a_k}$, where $p_i$ are distinct primes in ascending order and $a_i$ are positive integer exponents.