Prime factor
Encyclopedia : P : PR : PRI : Prime factor
In number theory, the prime factors of a positive integer are the prime numbers that divide into that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization.
Two positive integers are coprime if and only if they have no prime factors in common. The integer 1 is coprime to every positive integer, including itself. This is because it has no prime factors; it is the empty product.
The prime factorization of a positive integer is a list of the integer's prime factors, together with the maximum power of each prime factor that divides the integer exactly. The fundamental theorem of arithmetic says that every positive integer has a unique prime factorization.
For a positive integer n, the number of prime factors of n and the sum of the prime factors of n (not counting multiplicity) are examples of arithmetic functions of n that are additive but not completely additive.
Examples
- The prime factors of 6 are 3 and 2. (6 = 3 × 2)
- 5 has only one prime factor: itself. (5 is prime)
- 100 has two prime factors: 2 and 5. (100 = 22 × 52)
- 2, 4, 8, 16, etc. each have only one prime factor: 2. (2 is prime, 4 = 22, 8 = 23, etc.)
- 1 has no prime factors. ((1 is the empty product))
External links
- [Clickable table of prime factors for the first 1000 integers]
- [A Prime Factor Calculator. Can handle large numbers]
See also
From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.