See prime factor on Wiktionary
Download JSON data for prime factor meaning in All languages combined (6.9kB)
{
"forms": [
{
"form": "prime factors",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "prime factor (plural prime factors)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "61 39",
"kind": "topical",
"langcode": "en",
"name": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w+disamb"
}
],
"examples": [
{
"ref": "1847, James Robinson, The American Arithmetic, John P. Jewett & Co., page 91",
"text": "Hence, the prime factors of 100 are 1, 2, 2, 5, 5, and 1 × 2 × 2 × 5 × 5 = 100. From the above illustration, we derive the following rule for finding all the prime factors of any composite number.",
"type": "quotation"
},
{
"ref": "1994, Hans Riesel, Prime Numbers and Computer Methods for Factorization, Springer, page 161",
"text": "Theorem 5.5 Dickman's Theorem. The probability of a number N chosen at random having a prime factor between N#x5C;alpha and N#x7B;#x5C;alpha(1#x2B;#x5C;delta)#x7D; is approximately #x3D;#x5C;delta, independent of the magnitude of #x5C;alpha, if #x5C;delta is small.",
"type": "quotation"
},
{
"ref": "2003, Gary R. Jensen, Arithmetic for Teachers: With Applications and Topics from Geometry, American Mathematical Society, page 180",
"text": "If any subset of the set of prime factors of a be taken, then the product of the elements of this subset is a factor of a.\nFor example, 12 is a factor of 60 and the set of prime factors of 12 is {2, 2, 3}, which is a subset of {2, 2, 3, 5}, which is the set of prime factors of 60.",
"type": "quotation"
}
],
"glosses": [
"A factor of a given integer which is also a prime number."
],
"id": "en-prime_factor-en-noun-en:Q1137759",
"links": [
[
"number theory",
"number theory"
],
[
"factor",
"factor"
],
[
"integer",
"integer"
],
[
"prime number",
"prime number"
]
],
"raw_glosses": [
"(number theory) A factor of a given integer which is also a prime number."
],
"senseid": [
"en:Q1137759"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "factor",
"word": "質因數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "zhìyīnshù",
"sense": "factor",
"word": "质因数"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "factor",
"word": "prima faktoro"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "factor",
"word": "prima faktorigo"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "factor",
"word": "alkutekijä"
},
{
"code": "fr",
"lang": "French",
"sense": "factor",
"tags": [
"masculine"
],
"word": "facteur premier"
},
{
"code": "de",
"lang": "German",
"sense": "factor",
"tags": [
"masculine"
],
"word": "Primfaktor"
},
{
"code": "id",
"lang": "Indonesian",
"sense": "factor",
"word": "faktor prima"
},
{
"code": "ga",
"lang": "Irish",
"sense": "factor",
"tags": [
"masculine"
],
"word": "fachtóir príomha"
},
{
"code": "it",
"lang": "Italian",
"sense": "factor",
"tags": [
"masculine"
],
"word": "fattore primo"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "soinsū",
"sense": "factor",
"word": "素因数"
},
{
"code": "ms",
"lang": "Malay",
"sense": "factor",
"word": "faktor perdana"
},
{
"code": "gv",
"lang": "Manx",
"sense": "factor",
"tags": [
"masculine"
],
"word": "ard-faghteyr"
},
{
"code": "mi",
"lang": "Maori",
"sense": "factor",
"word": "tauwehe toitū"
},
{
"code": "no",
"lang": "Norwegian",
"sense": "factor",
"tags": [
"masculine"
],
"word": "primfaktor"
},
{
"code": "pl",
"lang": "Polish",
"sense": "factor",
"tags": [
"masculine"
],
"word": "czynnik pierwszy"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "factor",
"tags": [
"masculine"
],
"word": "factor prim"
},
{
"code": "ru",
"lang": "Russian",
"roman": "prostój delítelʹ",
"sense": "factor",
"word": "просто́й дели́тель"
}
],
"wikidata": [
"Q1137759"
]
}
],
"word": "prime factor"
}
{
"forms": [
{
"form": "prime factors",
"tags": [
"present",
"singular",
"third-person"
]
},
{
"form": "prime factoring",
"tags": [
"participle",
"present"
]
},
{
"form": "prime factored",
"tags": [
"participle",
"past"
]
},
{
"form": "prime factored",
"tags": [
"past"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "prime factor (third-person singular simple present prime factors, present participle prime factoring, simple past and past participle prime factored)",
"name": "en-verb"
}
],
"lang": "English",
"lang_code": "en",
"pos": "verb",
"senses": [
{
"categories": [
{
"_dis": "35 65",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "44 56",
"kind": "other",
"name": "English entries with topic categories using raw markup",
"parents": [
"Entries with topic categories using raw markup",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "39 61",
"kind": "other",
"name": "English terms with non-redundant non-automated sortkeys",
"parents": [
"Terms with non-redundant non-automated sortkeys",
"Entry maintenance"
],
"source": "w+disamb"
}
],
"examples": [
{
"ref": "2004, Fred N. Grayson, CliffsTestPrep Military Flight Aptitude Tests, Wiley, page 39",
"text": "Any composite number can be prime factored; that is, it can be written as a product of prime numbers (excluding 1) in one and only one way.[…]When prime factoring numbers, it is standard to rearrange the factors so that the numbers are in increasing order.",
"type": "quotation"
},
{
"ref": "2008, Phil Pine, Peterson's Master the SAT 2009, page 322",
"text": "For example, the number 30, which is not prime, can be prime factored as 2 x 3 x 5.",
"type": "quotation"
},
{
"ref": "2009, Jerome E. Kaufmann, Karen L. Schwitters, Elementary Algebra, 9th edition, Cengage Learning, page 386",
"text": "Another variation of the technique for changing radicals to simplest form is to prime factor the radicand and then to look for perfect squares in exponential form.",
"type": "quotation"
}
],
"glosses": [
"To reduce an integer to its set of prime factors."
],
"id": "en-prime_factor-en-verb-eIjK3vwX",
"links": [
[
"reduce",
"reduce"
]
],
"raw_glosses": [
"(transitive) To reduce an integer to its set of prime factors."
],
"related": [
{
"word": "prime factorization"
},
{
"word": "factorization"
},
{
"word": "prime decomposition"
},
{
"word": "prime element"
},
{
"word": "prime number"
},
{
"word": "unique factorization ring"
}
],
"tags": [
"transitive"
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "jakaa alkutekijöihin"
},
{
"code": "fr",
"lang": "French",
"sense": "Translations",
"word": "décomposer en facteurs premiers"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"tags": [
"imperfective"
],
"word": "rozkładać na czynniki pierwsze"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"tags": [
"perfective"
],
"word": "rozłożyć na czynniki pierwsze"
}
]
}
],
"word": "prime factor"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English entries with topic categories using raw markup",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with non-redundant non-automated sortkeys",
"English verbs",
"Translation table header lacks gloss",
"en:Number theory"
],
"forms": [
{
"form": "prime factors",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "prime factor (plural prime factors)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English terms with quotations",
"en:Number theory"
],
"examples": [
{
"ref": "1847, James Robinson, The American Arithmetic, John P. Jewett & Co., page 91",
"text": "Hence, the prime factors of 100 are 1, 2, 2, 5, 5, and 1 × 2 × 2 × 5 × 5 = 100. From the above illustration, we derive the following rule for finding all the prime factors of any composite number.",
"type": "quotation"
},
{
"ref": "1994, Hans Riesel, Prime Numbers and Computer Methods for Factorization, Springer, page 161",
"text": "Theorem 5.5 Dickman's Theorem. The probability of a number N chosen at random having a prime factor between N#x5C;alpha and N#x7B;#x5C;alpha(1#x2B;#x5C;delta)#x7D; is approximately #x3D;#x5C;delta, independent of the magnitude of #x5C;alpha, if #x5C;delta is small.",
"type": "quotation"
},
{
"ref": "2003, Gary R. Jensen, Arithmetic for Teachers: With Applications and Topics from Geometry, American Mathematical Society, page 180",
"text": "If any subset of the set of prime factors of a be taken, then the product of the elements of this subset is a factor of a.\nFor example, 12 is a factor of 60 and the set of prime factors of 12 is {2, 2, 3}, which is a subset of {2, 2, 3, 5}, which is the set of prime factors of 60.",
"type": "quotation"
}
],
"glosses": [
"A factor of a given integer which is also a prime number."
],
"links": [
[
"number theory",
"number theory"
],
[
"factor",
"factor"
],
[
"integer",
"integer"
],
[
"prime number",
"prime number"
]
],
"raw_glosses": [
"(number theory) A factor of a given integer which is also a prime number."
],
"senseid": [
"en:Q1137759"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"wikidata": [
"Q1137759"
]
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "factor",
"word": "質因數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "zhìyīnshù",
"sense": "factor",
"word": "质因数"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "factor",
"word": "prima faktoro"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "factor",
"word": "prima faktorigo"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "factor",
"word": "alkutekijä"
},
{
"code": "fr",
"lang": "French",
"sense": "factor",
"tags": [
"masculine"
],
"word": "facteur premier"
},
{
"code": "de",
"lang": "German",
"sense": "factor",
"tags": [
"masculine"
],
"word": "Primfaktor"
},
{
"code": "id",
"lang": "Indonesian",
"sense": "factor",
"word": "faktor prima"
},
{
"code": "ga",
"lang": "Irish",
"sense": "factor",
"tags": [
"masculine"
],
"word": "fachtóir príomha"
},
{
"code": "it",
"lang": "Italian",
"sense": "factor",
"tags": [
"masculine"
],
"word": "fattore primo"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "soinsū",
"sense": "factor",
"word": "素因数"
},
{
"code": "ms",
"lang": "Malay",
"sense": "factor",
"word": "faktor perdana"
},
{
"code": "gv",
"lang": "Manx",
"sense": "factor",
"tags": [
"masculine"
],
"word": "ard-faghteyr"
},
{
"code": "mi",
"lang": "Maori",
"sense": "factor",
"word": "tauwehe toitū"
},
{
"code": "no",
"lang": "Norwegian",
"sense": "factor",
"tags": [
"masculine"
],
"word": "primfaktor"
},
{
"code": "pl",
"lang": "Polish",
"sense": "factor",
"tags": [
"masculine"
],
"word": "czynnik pierwszy"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "factor",
"tags": [
"masculine"
],
"word": "factor prim"
},
{
"code": "ru",
"lang": "Russian",
"roman": "prostój delítelʹ",
"sense": "factor",
"word": "просто́й дели́тель"
}
],
"word": "prime factor"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English entries with topic categories using raw markup",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with non-redundant non-automated sortkeys",
"English verbs",
"Translation table header lacks gloss",
"en:Number theory"
],
"forms": [
{
"form": "prime factors",
"tags": [
"present",
"singular",
"third-person"
]
},
{
"form": "prime factoring",
"tags": [
"participle",
"present"
]
},
{
"form": "prime factored",
"tags": [
"participle",
"past"
]
},
{
"form": "prime factored",
"tags": [
"past"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "prime factor (third-person singular simple present prime factors, present participle prime factoring, simple past and past participle prime factored)",
"name": "en-verb"
}
],
"lang": "English",
"lang_code": "en",
"pos": "verb",
"related": [
{
"word": "prime factorization"
},
{
"word": "factorization"
},
{
"word": "prime decomposition"
},
{
"word": "prime element"
},
{
"word": "prime number"
},
{
"word": "unique factorization ring"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"English transitive verbs"
],
"examples": [
{
"ref": "2004, Fred N. Grayson, CliffsTestPrep Military Flight Aptitude Tests, Wiley, page 39",
"text": "Any composite number can be prime factored; that is, it can be written as a product of prime numbers (excluding 1) in one and only one way.[…]When prime factoring numbers, it is standard to rearrange the factors so that the numbers are in increasing order.",
"type": "quotation"
},
{
"ref": "2008, Phil Pine, Peterson's Master the SAT 2009, page 322",
"text": "For example, the number 30, which is not prime, can be prime factored as 2 x 3 x 5.",
"type": "quotation"
},
{
"ref": "2009, Jerome E. Kaufmann, Karen L. Schwitters, Elementary Algebra, 9th edition, Cengage Learning, page 386",
"text": "Another variation of the technique for changing radicals to simplest form is to prime factor the radicand and then to look for perfect squares in exponential form.",
"type": "quotation"
}
],
"glosses": [
"To reduce an integer to its set of prime factors."
],
"links": [
[
"reduce",
"reduce"
]
],
"raw_glosses": [
"(transitive) To reduce an integer to its set of prime factors."
],
"tags": [
"transitive"
]
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "jakaa alkutekijöihin"
},
{
"code": "fr",
"lang": "French",
"sense": "Translations",
"word": "décomposer en facteurs premiers"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"tags": [
"imperfective"
],
"word": "rozkładać na czynniki pierwsze"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"tags": [
"perfective"
],
"word": "rozłożyć na czynniki pierwsze"
}
],
"word": "prime factor"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-06 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.