Product of 4 Consecutive Integers is Divisible by 24
Jump to navigation
Jump to search
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
- 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 $2.2$: $14$