##  [Fundamental Theorem of Arithmetic](/fundamental-theorem-arithmetic) 

  ##  [Fundamental Theorem of Arithmetic](https://mathlogic.quantumdictionary.io/fundamental-theorem-arithmetic-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The theorem that every integer greater than one can be written as a product of prime numbers and that this factorization is unique up to the order of the factors (and up to multiplication by units ±1 in Z).

 

 

 

 

 





 

 



 ##  [Fundamental Theorem of Arithmetic](https://puremath.quantumdictionary.io/fundamental-theorem-arithmetic-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The statement that every integer greater than one factors uniquely as a product of prime numbers, up to ordering of the factors; primes are the multiplicative atoms of the integers.

 

 

 

 

 





 

 



 ##  [Fundamental Theorem of Arithmetic](https://algebra.quantumdictionary.io/fundamental-theorem-arithmetic-2) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The statement that every integer greater than one can be expressed as a product of prime numbers and that this factorization is unique up to the order of the prime factors.