Prime Factorization Calculator
Break any number into its prime factors with this prime factorization calculator. Includes a factor tree, divisor list, and GCD/LCM calculator.
About Prime Factorization Calculator
Prime factorization is a fundamental concept in number theory and an important building block for topics like GCD, LCM, and simplifying fractions. This calculator instantly decomposes any positive integer into its prime factors with proper exponent notation.
Visual Factor Tree
For numbers up to 100,000, the tool draws an interactive factor tree diagram using SVG. The tree starts with your number at the top and branches down with each division step. Prime factors are highlighted in indigo circles so you can spot them immediately.
Complete Divisor List
Besides the prime factors, the tool lists every divisor of the number. For example, 360 has 24 divisors ranging from 1 to 360. A summary card shows the count of distinct prime factors, total number of divisors, and whether the number is prime.
GCD and LCM Calculator
A bonus section below the main tool lets you enter two numbers to find their greatest common divisor and least common multiple. This is useful for simplifying fractions or finding common denominators - try the Fraction Calculator for full fraction arithmetic.
Privacy
All computation runs in your browser. Nothing is sent to any server. For solving equations that involve these factors, check out the Equation Solver.
Frequently Asked Questions
What is prime factorization?
Prime factorization is breaking a number down into the product of prime numbers. For example, 360 = 2^3 x 3^2 x 5. Every integer greater than 1 has a unique prime factorization (this is called the fundamental theorem of arithmetic).
What is a factor tree?
A factor tree is a diagram that visually shows how a number is split into smaller factors at each step until all remaining factors are prime. It starts with the original number at the top and branches downward with each division.
How large a number can this handle?
The factorization engine works for numbers up to about 1 trillion (10^12). The factor tree visualization is shown for numbers up to 100,000 to keep the diagram readable. The full divisor list is displayed for numbers up to 10 million.
How are GCD and LCM calculated?
The greatest common divisor (GCD) is found using the Euclidean algorithm, which repeatedly divides the larger number by the smaller until the remainder is zero. The least common multiple (LCM) is then computed as |a x b| / GCD(a, b).
How do I know if a number is prime?
A prime number is only divisible by 1 and itself. The calculator checks this and shows a highlighted badge if your number is prime. Its factorization will simply be the number itself.