2009 UNCO Math Contest II Problems/Problem 4

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 $2^7\cdot3^2\cdot5\cdot7$ .

2009 UNCO Math Contest II (Problems • Answer Key • Resources)
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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2009 UNCO Math Contest II Problems/Problem 4

Problem

Solution

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