prime factor

plural prime factors

1. mathematicsA factor of a given integer which is also a prime number.

   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.

   1847, James Robinson, The American Arithmetic, John P. Jewett & Co., page 91

   2 more examples

   Theorem 5.5 Dickman's Theorem. The probability of a number N chosen at random having a prime factor between N#92;alpha and N#123;#92;alpha(1#43;#92;delta)#125; is approximately #61;#92;delta, independent of the magnitude of #92;alpha, if #92;delta is small.

   1994, Hans Riesel, Prime Numbers and Computer Methods for Factorization, Springer, page 161

   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.

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

2. Used other than figuratively or idiomatically: see prime, factor.

   It became apparent to me that Mr. Genthner's open profession of being gay was the prime factor in his conviction and sentencing.

   1989 February 12, anonymous author, “Innocent Man In Prison Because He Is Gay”, in Gay Community News, volume 16, number 30, page 5

present singular third person prime factors · participle present prime factoring · participle past prime factored · past prime factored

1. transitiveTo reduce an integer to its set of prime factors.

   For example, the number 30, which is not prime, can be prime factored as 2 x 3 x 5.

   2008, Phil Pine, Peterson's Master the SAT 2009, page 322

   2 more examples

   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.

   2004, Fred N. Grayson, CliffsTestPrep Military Flight Aptitude Tests, Wiley, page 39

   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.

   2009, Jerome E. Kaufmann, Karen L. Schwitters, Elementary Algebra, 9th edition, Cengage Learning, page 386