Factorials: Level 2 Challenges Practice Problems Online

Which of these numbers is a perfect square?

\dfrac{14! \cdot 15!}{2}

\dfrac{15! \cdot 16!}{2}

\dfrac{16! \cdot 17!}{2}

\dfrac{17! \cdot 18!}{2}

\dfrac{18! \cdot 19!}{2}

What is the product of all positive odd integers less than $10000$ ?

\dfrac{10000!}{(5000!)^2}

\dfrac{10000!}{2^{5000}\cdot5000!}

\dfrac{9999!}{2^{5000}}

\dfrac{10000!}{2^{5000}}

\dfrac{5000!}{2^{5000}}

$\large 1 \cdot 1! + 2\cdot 2! + 3\cdot 3! + \cdots + 25\cdot 25! = \, ?$

Which is greater?

$300! \text{ or } 100^{300} ?$

Given that $13!= 13 \times 12 \times 11 \times \cdot \cdot \cdot \times 2 \times 1 = 6227020800$ , it can be seen that $13!$ contains two trailing zeroes.

How many trailing zeroes does $1000!$ contain?

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Factorials: Level 2 Challenges