Find largest natural number that exactly divides the product of any four consecutive natural no s is ?121824None

The largest natural number that exactly divides the product of any four consecutive natural numbers is 24.

Here's why:

Let's take any four consecutive natural numbers. We can represent them as n, n+1, n+2, n+3.

Since these are consecutive numbers, at least one of them must be divisible by 2 (even number) and at least one must be divisible by 3.

Also, among any four consecutive numbers, there must be at least one pair of numbers that are both even. This means that the product of these four numbers is divisible by 2*2 = 4.

So, the product of any four consecutive numbers is always divisible by 223 = 12.

But, if n is a multiple of 4, then the product will be divisible by 222*3 = 24.

So, the largest natural number that exactly divides the product of any four consecutive natural numbers is 24.