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Question

(C) The product of $n$ consecutive natural numbers is always divisible by $n!$ (n factorial).For $n = 4$,the product of any four consecutive natural n

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(C) The product of $n$ consecutive natural numbers is always divisible by $n!$ (n factorial).For $n = 4$,the product of any four consecutive natural numbers is divisible by $4!$.$4! = 1 	imes 2 	imes 3 	imes 4 = 24$.To verify,consider the first four natural numbers: $1 	imes 2 	imes 3 	imes 4 = 24$.Consider the next set: $2 	imes 3 	imes 4 	imes 5 = 120$,which is also divisible by $24$ $(120 / 24 = 5)$.Therefore,the largest natural number that divides the product of any four consecutive natural numbers is $24$.

The largest natural number which exactly divides the product of any four consecutive natural numbers is

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