Number Theory

Factorials

Factorials: Level 2 Challenges

         

Which of these numbers is a perfect square?

What is the product of all positive odd integers less than 1000010000?

11!+22!+33!++2525!=?\large 1 \cdot 1! + 2\cdot 2! + 3\cdot 3! + \cdots + 25\cdot 25! = \, ?

Which is greater?

300! or 100300? 300! \text{ or } 100^{300} ?

Given that 13!=13×12×11××2×1=622702080013!= 13 \times 12 \times 11 \times \cdot \cdot \cdot \times 2 \times 1 = 6227020800 , it can be seen that 13!13! contains two trailing zeroes.

How many trailing zeroes does 1000!1000! contain?

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