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# Factorials

2! = 2, 3! = 3*2, 4! = 4*3*2… and 100! is a lot better than writing out 158 digits. 90! is the largest factorial that can fit in a tweet.

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?

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

\[x! = 3! \times 5!\] What is \(x?\)

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