Product of 5 Consecutive Integers is Divisible by 120

Theorem

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

Then their product $a b c d e$ is divisible by $120$.

Proof

This is an application of Divisibility of Product of Consecutive Integers with $n = 5$.

By the theorem, the product of $5$ consecutive integers is divisible by $5! = 120$.

$\blacksquare$

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 $2.2$: $14$