This prime factorization calculator allows you to enter a composite number, and it produces a list of the prime numbers that, when multiplied, produce the original composite number. Use this factorization calculator to produce a factor tree, or just determine the list of primes that divide a given integer.

The factor tree produced by the site’s prime factorization calculator shows the prime values as highlighted nodes. Each prime factor is assigned a unique color, and the occurrences of the each prime factor correspond to the exponent on the same prime in the prime factorization in the canonical factorization shown below the factor tree.

There are many potential ways to produce a prime factorization, but some of them, especially those that start with small primes, produce very repetitive factor trees. The algorithm used by this prime factorization calculator starts it’s search for factors at the square root of the input and then checks for increasingly smaller factors. This will reuse a prime factorization of internal composite numbers more frequently and produces factor trees that are somewhat more compact (and elegant) than more naïve approaches.

Use the ‘Zoom’ button to highlight only the calculator on this page. That makes using this prime factorization calculator on smart boards or projectors in a classroom setting less distracting.

To understand what prime factorization is good for, it helps to start with the very nature of numbers and how their prime factors are used to create them.

Here's a brief video about our Prime Factorization Calculator - https://www.youtube.com/watch?v=TzgQJsSYhRU