10
votes
4answers
772 views

Highest power of a prime $p$ dividing $N!$

How does one find the highest power of a prime $p$ that divides $N!$ and other related products? Related question: How many zeros are there at the end of $N!$? This is being done to reduce ...
4
votes
9answers
1k views

Prove $0! = 1$ from first principles

How can I prove from first principles that $0!$ is equal to $1$?