##  [Legendre's Formula](/legendres-formula) 

  ##  [Legendre's Formula](https://puremath.quantumdictionary.io/legendres-formula-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A formula giving the exponent of a prime p dividing n!: v_p(n!) = sum_{k≥1} floor(n/p^k), i.e., the p-adic valuation of n! equals the sum of the integer parts of n divided by successive powers of p until those terms vanish.