Product of 4 Consecutive Integers is Divisible by 24

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Theorem

Let $a, b, c, d \in \Z$ be consecutive integers.

Then their product $a b c d$ is divisible by $24$.


Proof

This is an application of Divisibility of Product of Consecutive Integers with $n = 4$.

By the theorem, the product of $4$ consecutive integers is divisible by $4! = 24$.

$\blacksquare$


Sources