prime factor

Noun

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Noun

**prime factor** (*plural* prime factors)

- (
*number theory*) A factor of a given integer which is also a prime number.**1847**, James Robinson,*The American Arithmetic*, John P. Jewett & Co., page 91 ↗,- 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.

- Hence, the
**1994**, Hans Riesel,*Prime Numbers and Computer Methods for Factorization*, Springer, page 161 ↗,**Theorem 5.5 Dickman's Theorem.**The probability of a number N chosen at random having a**prime factor**between N^\alpha and N^{\alpha(1+\delta)} is approximately =\delta,*independent of the magnitude of*\alpha, if \delta is small.

**2003**, Gary R. Jensen,*Arithmetic for Teachers: With Applications and Topics from Geometry*, American Mathematical Society, page 180 ↗,*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.- For 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.

- German: Primfaktor
- Italian: fattore primo
- Russian: просто́й дели́тель

**prime factor** (prime factors, *present participle* prime factoring; *past and past participle* prime factored)

- (
*transitive*) to reduce an integer to its set of prime factors.**2004**, Fred N. Grayson,*CliffsTestPrep Military Flight Aptitude Tests*, Wiley, page 39 ↗,- 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.

- Any composite number can be
**2008**, Phil Pine,*Peterson's Master the SAT 2009*, page 322 ↗,- For example, the number 30, which is not prime, can be
**prime factored**as 2 x 3 x 5.

- For example, the number 30, which is not prime, can be
**2009**, Jerome E. Kaufmann, Karen L. Schwitters,*Elementary Algebra*, Cengage Learning, 9th Edition, page 386 ↗,- 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.

- Another variation of the technique for changing radicals to simplest form is to

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