The numbers which cannot be factored in are called prime numbers. Prime numbers have two factors only, one and the number itself. This means that prime numbers are divisible only by one and the number itself.
Primality is the property of being prime. One can check the primality of a number by trial division test. Start with the smallest number and then increase the number to do the trial division test. One can also find the divisibility of a number by simple rules of divisibility. Prime numbers have wide applicability in various fields of science and technology. Prime numbers are used in abstract algebra, Eisenstein’s criterion, computing for checksums, hash tables, pseudorandom number generators, knot theory, quantum mechanics, evolutionary biology, arts, and literature.
Consider an example, 34866. Its factors are 2 x 3 x 3 x 13 x 149. All these numbers are prime numbers. Hence, these are called prime factors.
The numbers having more than two factors are called composite numbers. Composite numbers must have factors other than one and the number itself. They are also known as non-prime numbers.
It states that every number greater than 1 can be written as a product of two or more prime numbers.