You can even take this further. As you can see in Chelsea's example above, among three consecutive integers you not only find a multiple of 3 somewhere -- you also must have at least one multiple of 2. So the product of three consecutive integers will always be divisible by 3*2, or in other words, by 3! (three factorial).

If instead you look at four consecutive numbers, you'll always have exactly one multiple of 4, at least one multiple of 3, and another number which is a multiple of 2, so the product of four consecutive integers is always divisible by 4*3*2, or in other words by 4!

And that's a general rule: the product of n consecutive integers is always divisible by n!

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