Difference between revisions of "2009 UNCO Math Contest II Problems/Problem 4"

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example, <math>4!</math> means <math>4\cdot 3\cdot 2\cdot 1</math>)
 
example, <math>4!</math> means <math>4\cdot 3\cdot 2\cdot 1</math>)
  
== Solution ==
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== Solution ==
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We first factorize the product as <math>2^7\cdot3^2\cdot5\cdot7</math>.
  
 
== See also ==
 
== See also ==

Revision as of 22:47, 25 November 2016

Problem

How many perfect squares are divisors of the product $1!\cdot 2!\cdot 3!\cdot 4!\cdot 5!\cdot 6!\cdot 7!\cdot 8!$ ? (Here, for example, $4!$ means $4\cdot 3\cdot 2\cdot 1$)

Solution

We first factorize the product as $2^7\cdot3^2\cdot5\cdot7$.

See also

2009 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions
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