fundamental theorem of arithmetic

theorem about prime factorization of a number

Intangible theorem Q670235

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Summary

fundamental theorem of arithmetic is a theorem^[1]. It ranks in the top 4% of theorem entities by monthly Wikipedia readership (3,167 views/month).^[2]

Key Facts

Commons category: Fundamental theorem of arithmetic^[3]
Main subject: integer factorization^[4], unique factorization domain^[5]
Described by source: Mathwords^[6], AoPS Wiki^[7]
Different from: fundamental theorem of algebra^[8]
Studied by: number theory^[9]
On focus list of Wikimedia project: Wikipedia:Vital articles/Level/4^[10]
Maintained by WikiProject: WikiProject Mathematics^[11]

Why It Matters

fundamental theorem of arithmetic has Wikipedia articles in 30 language editions, a strong signal of global cultural recognition.^[12] It is known by 39 alternative names across languages and contexts.^[13]

⭐ Popularity Graph

30/100 established

🌐 Wiki Languages

70 / 428 langs top 1%

📈 Wikipedia Views · last 870h

4.9K/mo 19.7K/yr

🔗 Readers Also Explored · clickstream

252

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fundamental theorem of algebra

Fermat's Last Theorem

Quick Facts

Instance of theorem

Properties

Defining formula ((a \in \mathbb{Z}\backslash\{0,1,-1\}) \land (p \in \mathbb{P}) \land (e_i \geq 1) \land (i \neq j \implies p_i \neq p_j)) \implies \exists! p_1, p_2, \dotsc , p_r, e_1, e_2, \dotsc , e_r : a=\pm p_i^{e_1}p_2^{e_2} \dotsm p_r^{e_r}

Described by source Mathwords, AoPS Wiki

Different from fundamental theorem of algebra

Main subject integer factorization, unique factorization domain

Maintained by wikiproject WikiProject Mathematics

On focus list of wikimedia project Wikipedia:Vital articles/Level/4

Studied by number theory

External References (12)

Brilliant wiki id fundamental-theorem-of-arithmetic

Encyclopædia britannica online id topic/fundamental-theorem-of-arithmetic

Freebase id /m/0325_

Mathworld id FundamentalTheoremofArithmetic

Metamath statement id 1arith

Microsoft academic id (discontinued) 68625148

Namuwiki id 산술의 기본정리

Nlab id fundamental theorem of arithmetic

Planetmath id FundamentalTheoremOfArithmetic

Quora topic id Fundamental-Theorem-of-Arithmetic

Treccani's enciclopedia della matematica id teorema-fondamentale-dell-aritmetica

Vikidia article id fr:Théorème_fondamental_de_l'arithmétique

🌐 Available in 30 languages

enFundamental theorem of arithmetic arالمبرهنة الأساسية في الحسابيات csZákladní věta aritmetiky daAritmetikkens fundamentalsætning deFundamentalsatz der Arithmetik elΘεμελιώδες θεώρημα αριθμητικής esTeorema fundamental de la aritmética faقضیه اساسی حساب fiAritmetiikan peruslause frThéorème fondamental de l'arithmétique heהמשפט היסודי של האריתמטיקה hiअङ्कगणित का मूलभूत प्रमेय huA számelmélet alaptétele idTeorema dasar aritmetika itTeorema fondamentale dell'aritmetica ja算術の基本定理 ko산술의 기본 정리 msTeorem asas aritmetik nlHoofdstelling van de rekenkunde noAritmetikkens fundamentalteorem plZasadnicze twierdzenie arytmetyki ptTeorema fundamental da aritmética roTeorema fundamentală a aritmeticii ruОсновная теорема арифметики svAritmetikens fundamentalsats thทฤษฎีบทมูลฐานของเลขคณิต trAritmetiğin temel teoremi ukОсновна теорема арифметики viĐịnh lý cơ bản của số học zh算术基本定理

🏷️ Also known as

en prime factorisation theorem en unique-prime-factorization theorem en unique factorization theorem en unique factorisation theorem en prime factorization theorem en FTA en fundamental theorem of arithmetic ar المبرهنة الأساسية في الحسابيات cs základní věta aritmetiky da Aritmetikkens fundamentalsætning de Fundamentalsatz der Arithmetik el Θεμελιώδες θεώρημα αριθμητικής es teorema fundamental de la aritmética es teorema fundamental de la aritmetica fa قضیه اساسی حساب fi Aritmetiikan peruslause fr théorème fondamental de l'arithmétique he המשפט היסודי של האריתמטיקה hi अङ्कगणित का मूलभूत प्रमेय hu a számelmélet alaptétele

🔗 Connections

Main subject 2

integer factorization, unique factorization domain

Different from 1

fundamental theorem of algebra

Instance of 1

theorem

Maintained by wikiproject 1

WikiProject Mathematics

On focus list of wikimedia project 1

Wikipedia:Vital articles/Level/4

Studied by 1

number theory

← Different from 1

fundamental theorem of algebra

← Generalization of 1

primary decomposition

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

Class ancestry

[1] ↑ fundamental theorem of arithmetic is an instance of theorem (Q65943) [P31, primary]. Wikidata. wikidata.org.

Aggregate / graph-position facts

[2] ↑ fundamental theorem of arithmetic ranks in the top 4% of theorem entities by monthly Wikipedia readership (3,167 views/month).. Wikimedia Foundation. dumps.wikimedia.org.
[12] ↑ fundamental theorem of arithmetic has Wikipedia articles in 30 language editions, a strong signal of global cultural recognition.. Wikidata sitelinks. wikidata.org.
[13] ↑ fundamental theorem of arithmetic is known by 39 alternative names across languages and contexts.. Wikidata aliases. wikidata.org.

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APA

4ort.xyz Knowledge Graph. (2026). fundamental theorem of arithmetic. Retrieved October 17, 2026, from https://4ort.xyz/entity/fundamental-theorem-of-arithmetic

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“fundamental theorem of arithmetic.” 4ort.xyz Knowledge Graph, 4ort.xyz, 17 Oct. 2026, https://4ort.xyz/entity/fundamental-theorem-of-arithmetic.

BibTeX

@misc{4ortxyz_fundamental-theorem-of-arithmetic_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{fundamental theorem of arithmetic}}, year = {2026}, url = {https://4ort.xyz/entity/fundamental-theorem-of-arithmetic}, note = {Accessed: 2026-10-17}}

LLM prompt

According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): fundamental theorem of arithmetic — https://4ort.xyz/entity/fundamental-theorem-of-arithmetic (retrieved 2026-10-17)

Canonical URL: https://4ort.xyz/entity/fundamental-theorem-of-arithmetic · Last refreshed: October 17, 2026

Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

17d ago · AddyLockPool · 2026-10-02 view diff on Wikidata ↗

Described by source → Mathwords, AoPS Wiki

Sitelink count → 70

Wikipedia languages → ['als', 'ar', 'ast', 'bg', 'bn', 'ca', 'commons', 'cs', 'cv', 'da', 'de', 'el',

Planetmath id → FundamentalTheoremOfArithmetic

+ 1 other property edited (see Wikidata diff for full list)

"/* wbeditentity-statements-multiple-properties-add:0||2 */ Add 2 sources/identifiers (via Wikidata Source Saver)"
4w ago · AddyLockPool · 2026-09-15 view diff on Wikidata ↗

Maintained by wikiproject → WikiProject Mathematics

Different from → fundamental theorem of algebra

Studied by → number theory

Instance of → theorem

+ 5 other properties edited (see Wikidata diff for full list)

"/* wbsetclaim-create:2||1 */ Described by source: Mathwords"

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