prime factor

prime factor (plural prime factors)

  1. (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.
    • 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.
Translations Verb

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

  1. (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.
    • 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.
    • 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.
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