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 [[prime|primes]] | + | 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, the <math>p_{i}</math> are prime numbers, and the <math>e_i</math> are their integral exponents. |
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 12:33, 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, the 
are prime numbers, and the 
are their integral exponents.
Prime factorizations are important in many ways, for instance, to simplify fractions.
