Definitions for prime factor
prime fac·tor

Princeton's WordNetRate this definition:4.7 / 3 votes

1. prime factornoun

   the prime factors of a quantity are all of the prime quantities that will exactly divide the given quantity

WiktionaryRate this definition:5.0 / 2 votes

1. prime factornoun

   A factor of a given integer which is also a prime number.

2. prime factorverb

   to reduce an integer to its set of prime factors

WikipediaRate this definition:0.0 / 0 votes

1. prime factor

   A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n {\displaystyle n} , called trial division, tests whether n {\displaystyle n} is a multiple of any integer between 2 and n {\displaystyle {\sqrt {n}}} . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of December 2018 the largest known prime number is a Mersenne prime with 24,862,048 decimal digits.There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen large number being prime is inversely proportional to its number of digits, that is, to its logarithm. Several historical questions regarding prime numbers are still unsolved. These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals.

ChatGPTRate this definition:0.0 / 0 votes

1. prime factor

   A prime factor is a factor of a number that is a prime number itself. A prime number is a natural number greater than 1 that can only be divided by 1 and itself without leaving a remainder. Prime factors are the building blocks of all numbers, as they are the smallest prime numbers which, when multiplied together, form that number.

WikidataRate this definition:3.0 / 2 votes

1. Prime factor

   In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. The process of finding these numbers is called integer factorization, or prime factorization. A prime factor can be visualized by understanding Euclid's geometric position. He saw a whole number as a line segment, which has a smallest line segment greater than 1 that can divide equally into it. For a prime factor p of n, the multiplicity of p is the largest exponent a for which pa divides n. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicity. The fundamental theorem of arithmetic says that every positive integer has a unique prime factorization. To shorten prime factorization, numbers are often expressed in powers, so For a positive integer n, the number of prime factors of n and the sum of the prime factors of n are examples of arithmetic functions of n that are additive but not completely additive. Determining the prime factors of a number is an example of a problem frequently used to ensure cryptographic security in encryption systems; this problem is believed to require super-polynomial time in the number of digits — it is relatively easy to construct a problem that would take longer than the known age of the Universe to solve on current computers using current algorithms.

Matched Categories

1. • Divisor

How to pronounce prime factor?

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How to say prime factor in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of prime factor in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of prime factor in Pythagorean Numerology is: 7

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=prime factor
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Prime_Factor
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Prime_Factor
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=prime factor