Number Theory
# Factorials

Which of these numbers is a perfect square?

What is the product of all positive odd integers less than \(10000\)?

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

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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