Number Theory
# Factorials

Which of the following is equal to $\Large \frac{6!}{6}$?

What is the smallest positive integer $n$ such that $n!$ has exactly 1 trailing zero?

**Note**: Trailing zeros are sequences of zeros that come at the end of a number. For example, 1,000 has 3 trailing zeros and 1,001 has no trailing zeros.

What is the smallest value of $n$ such that $n!$ is divisible by 9?

**Note:** If $n$ is a positive integer,
$n! = 1 \times 2 \times 3 \times \cdots \times (n - 1) \times n.$
For example,
$5! = 1 \times 2 \times 3 \times 4 \times 5.$

Are there 3 consecutive positive integers whose product is *not* divisible by $3! \, ?$

$x! = 3! \times 5!$ What is $x?$