2009 UNCO Math Contest II Problems/Problem 4

Revision as of 22:47, 25 November 2016 by Mathisfun04 (talk | contribs) (Solution)

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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