# Difference between revisions of "Prime factorization"

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− | By the [[Fundamental Theorem of Arithmetic]], every positive integer has a unique prime factorization. What is a prime factorization? It is a representation of a number in terms of powers of primes (it is of the form <math>{p_1}^{e_1}\cdot</math><math>{p_2}^{e_2}\cdot{p_3}^{e_3}\cdots{p_k}^{e_k} = n</math>, where ''n'' is any natural number). | + | By the [[Fundamental Theorem of Arithmetic]], every positive integer has a unique prime factorization. What is a prime factorization? It is a representation of a number in terms of powers of [[prime|primes]] (it is of the form <math>{p_1}^{e_1}\cdot</math><math>{p_2}^{e_2}\cdot{p_3}^{e_3}\cdots{p_k}^{e_k} = n</math>, where ''n'' is any natural number). |

Prime factorizations are important in many ways, for instance, to simplify [[fractions]]. | Prime factorizations are important in many ways, for instance, to simplify [[fractions]]. | ||

===Example Problem=== | ===Example Problem=== |

## Revision as of 06:45, 21 June 2006

By the Fundamental Theorem of Arithmetic, every positive integer has a unique prime factorization. What is a prime factorization? It is a representation of a number in terms of powers of primes (it is of the form , where *n* is any natural number).
Prime factorizations are important in many ways, for instance, to simplify fractions.