英和和英

名詞

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 ${\displaystyle N}$ chosen at random having a prime factor between ${\displaystyle N^{\alpha }}$ and ${\displaystyle N^{\alpha (1+\delta )}}$ is approximately ${\displaystyle =\delta }$, independent of the magnitude of ${\displaystyle \alpha }$, if ${\displaystyle \delta }$ 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.

2. Used other than figuratively or idiomatically: see prime,‎ factor.
   • 1989 February 12, anonymous author, “Innocent Man In Prison Because He Is Gay”, in Gay Community News, volume 16, number 30, page 5:

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