Prime Factorization Calculator
Find the prime factors, exponential decomposition, and factor tree for any integer up to $10^{13}$.
Results
Prime Factors of
Exponential Decomposition
CSV List of Prime Factors
Prime Number Index
| Factor | Index (Prime[n]) | Occurrence |
|---|
Prime index is shown for the first 500 prime numbers.
Factorization Tree
The numbers at the bottom (highlighted) are the final prime factors.
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What is Prime Factorization?
Prime factorization or integer factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number. This is also known as prime decomposition.
Prime Factorization by Trial Division
Say you want to find the prime factors of $100$ using trial division. Start by testing each integer to see if and how often it divides $100$ and the subsequent quotients evenly. The resulting set of factors will be prime since, for example, when $2$ is exhausted all multiples of $2$ are also exhausted.
Find the prime factors of $100$:
- $100 \div 2 = 50$; save $2$
- $50 \div 2 = 25$; save $2$
- $25 \div 5 = 5$; save $5$
- $5 \div 5 = 1$; save $5$
List the resulting prime factors as a sequence of multiples, $2 \times 2 \times 5 \times 5$ or as factors with exponents, $2^2 \times 5^2$.