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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.

# Factorials Warmup

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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