Explanation:

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization. A prime factor can be visualized by understanding Euclid's geometric position. He saw a whole number as a line segment, which has a smallest line segment greater than 1 that can divide equally into it.

For a prime factor p of n, the multiplicity of p is the largest exponent  a for which p^a divides n. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicity. The fundamental theorem of arithmetic says that every positive integer has a unique prime factorization.

In number theory, integer factorization or prime factorization is the breaking down of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer. (Our solved example in mathguru.com uses this concept).

To shorten prime factorization, numbers are often expressed in powers, so

http://en.wikipedia.org/wiki/Prime_factor

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