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  4. The greatest positive integer. which divides (n+16)(n+17)(n+18)(n+19), for all n ∈ N, is-

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Q. The greatest positive integer. which divides $(n+16)(n+17)(n+18)(n+19)$, for all $n \in N$, is-

Principle of Mathematical Induction

Solution:

Since product of any $r$ consecutive integers (क्रमागत पूर्णांक) is divisible by $r$ ! and not divisible by $r +1 !$
So given product of 4 consecutive integers is divisible by $4 !$ or 24 .