Product of 3 Consecutive Integers is Divisible by 6

Theorem

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

Then their product $a b c$ is divisible by $6$.

Proof

This is an application of Divisibility of Product of Consecutive Integers with $n = 3$.

By the theorem, the product of $3$ consecutive integers is divisible by $3! = 6$.

$\blacksquare$

Sources

• 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.2$ The Greatest Common Divisor: Problems $2.2$: $14$